[{"data":1,"prerenderedAt":3357},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum":546,"formula-related-de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum":3344},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":554,"category":208,"checks":3235,"conditions":979,"conditionsHtml":3263,"deprecated":3264,"description":3229,"extension":3265,"figure":3266,"figureCaption":3267,"figureHtml":3308,"formulaId":3309,"latex":3310,"latexHtml":3311,"level":3312,"meta":3313,"navigation":3278,"path":3314,"redirectFrom":3315,"related":3316,"seo":3321,"stem":3322,"subject":592,"summary":3323,"tags":3324,"variables":3329,"__hash__":3343},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum.md","Exponentielles Wachstum",[550,551,552,553],"Wachstumsformel","exponentielle Zunahme","prozentuales Wachstum","Wachstumsrate",{"type":555,"value":556,"toc":3228},"minimark",[557,562,578,770,1085,1205,1209,1313,1540,1654,1904,2063,2227,2402,2406],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,570,571,574,575],"p",{},"Von ",[567,568,569],"strong",{},"exponentiellem Wachstum"," spricht man, wenn ein Bestand in gleichen Zeitabständen um ",[567,572,573],{},"denselben Prozentsatz"," zunimmt. Pro Zeitschritt multipliziert man mit dem ",[567,576,577],{},"Wachstumsfaktor",[579,580,583],"span",{"className":581},[582],"katex-display",[579,584,587,630],{"className":585},[586],"katex",[579,588,591],{"className":589},[590],"katex-mathml",[592,593,596],"math",{"xmlns":594,"display":595},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[597,598,599,625],"semantics",{},[600,601,602,606,610,614,617],"mrow",{},[603,604,605],"mi",{},"q",[607,608,609],"mo",{},"=",[611,612,613],"mn",{},"1",[607,615,616],{},"+",[618,619,620,622],"mfrac",{},[603,621,563],{},[611,623,624],{},"100",[626,627,629],"annotation",{"encoding":628},"application\u002Fx-tex","q = 1 + \\frac{p}{100}",[579,631,635,662,683],{"className":632,"ariaHidden":634},[633],"katex-html","true",[579,636,639,644,650,655,659],{"className":637},[638],"base",[579,640],{"className":641,"style":643},[642],"strut","height:0.625em;vertical-align:-0.1944em;",[579,645,605],{"className":646,"style":649},[647,648],"mord","mathnormal","margin-right:0.0359em;",[579,651],{"className":652,"style":654},[653],"mspace","margin-right:0.2778em;",[579,656,609],{"className":657},[658],"mrel",[579,660],{"className":661,"style":654},[653],[579,663,665,669,672,676,680],{"className":664},[638],[579,666],{"className":667,"style":668},[642],"height:0.7278em;vertical-align:-0.0833em;",[579,670,613],{"className":671},[647],[579,673],{"className":674,"style":675},[653],"margin-right:0.2222em;",[579,677,616],{"className":678},[679],"mbin",[579,681],{"className":682,"style":675},[653],[579,684,686,690],{"className":685},[638],[579,687],{"className":688,"style":689},[642],"height:1.7936em;vertical-align:-0.686em;",[579,691,693,698,766],{"className":692},[647],[579,694],{"className":695},[696,697],"mopen","nulldelimiter",[579,699,701],{"className":700},[618],[579,702,706,757],{"className":703},[704,705],"vlist-t","vlist-t2",[579,707,710,752],{"className":708},[709],"vlist-r",[579,711,715,729,740],{"className":712,"style":714},[713],"vlist","height:1.1076em;",[579,716,718,723],{"style":717},"top:-2.314em;",[579,719],{"className":720,"style":722},[721],"pstrut","height:3em;",[579,724,726],{"className":725},[647],[579,727,624],{"className":728},[647],[579,730,732,735],{"style":731},"top:-3.23em;",[579,733],{"className":734,"style":722},[721],[579,736],{"className":737,"style":739},[738],"frac-line","border-bottom-width:0.04em;",[579,741,743,746],{"style":742},"top:-3.677em;",[579,744],{"className":745,"style":722},[721],[579,747,749],{"className":748},[647],[579,750,563],{"className":751},[647,648],[579,753,756],{"className":754},[755],"vlist-s","​",[579,758,760],{"className":759},[709],[579,761,764],{"className":762,"style":763},[713],"height:0.686em;",[579,765],{},[579,767],{"className":768},[769,697],"mclose",[563,771,772,773,776,777,805,806,835,836,888,889,955,956,1014,1015,1043,1044,1084],{},"Bei einer ",[567,774,775],{},"Abnahme"," ist ",[579,778,780,793],{"className":779},[586],[579,781,783],{"className":782},[590],[592,784,785],{"xmlns":594},[597,786,787,791],{},[600,788,789],{},[603,790,563],{},[626,792,563],{"encoding":628},[579,794,796],{"className":795,"ariaHidden":634},[633],[579,797,799,802],{"className":798},[638],[579,800],{"className":801,"style":643},[642],[579,803,563],{"className":804},[647,648]," negativ, der Faktor also kleiner als ",[579,807,809,822],{"className":808},[586],[579,810,812],{"className":811},[590],[592,813,814],{"xmlns":594},[597,815,816,820],{},[600,817,818],{},[611,819,613],{},[626,821,613],{"encoding":628},[579,823,825],{"className":824,"ariaHidden":634},[633],[579,826,828,832],{"className":827},[638],[579,829],{"className":830,"style":831},[642],"height:0.6444em;",[579,833,613],{"className":834},[647],": ",[579,837,839,865],{"className":838},[586],[579,840,842],{"className":841},[590],[592,843,844],{"xmlns":594},[597,845,846,862],{},[600,847,848,851,854,858],{},[607,849,850],{},"−",[611,852,853],{},"15",[855,856,857],"mtext",{}," ",[603,859,861],{"mathvariant":860},"normal","%",[626,863,864],{"encoding":628},"-15\\,\\%",[579,866,868],{"className":867,"ariaHidden":634},[633],[579,869,871,875,878,881,885],{"className":870},[638],[579,872],{"className":873,"style":874},[642],"height:0.8333em;vertical-align:-0.0833em;",[579,876,850],{"className":877},[647],[579,879,853],{"className":880},[647],[579,882],{"className":883,"style":884},[653],"margin-right:0.1667em;",[579,886,861],{"className":887},[647]," pro Jahr ergibt ",[579,890,892,911],{"className":891},[586],[579,893,895],{"className":894},[590],[592,896,897],{"xmlns":594},[597,898,899,908],{},[600,900,901,903,905],{},[603,902,605],{},[607,904,609],{},[611,906,907],{},"0,85",[626,909,910],{"encoding":628},"q = 0{,}85",[579,912,914,932],{"className":913,"ariaHidden":634},[633],[579,915,917,920,923,926,929],{"className":916},[638],[579,918],{"className":919,"style":643},[642],[579,921,605],{"className":922,"style":649},[647,648],[579,924],{"className":925,"style":654},[653],[579,927,609],{"className":928},[658],[579,930],{"className":931,"style":654},[653],[579,933,935,939,943,951],{"className":934},[638],[579,936],{"className":937,"style":938},[642],"height:0.8389em;vertical-align:-0.1944em;",[579,940,942],{"className":941},[647],"0",[579,944,946],{"className":945},[647],[579,947,950],{"className":948},[949],"mpunct",",",[579,952,954],{"className":953},[647],"85",". Die Bedingung ",[579,957,959,980],{"className":958},[586],[579,960,962],{"className":961},[590],[592,963,964],{"xmlns":594},[597,965,966,977],{},[600,967,968,970,973,975],{},[603,969,563],{},[607,971,972],{},">",[607,974,850],{},[611,976,624],{},[626,978,979],{"encoding":628},"p > -100",[579,981,983,1002],{"className":982,"ariaHidden":634},[633],[579,984,986,990,993,996,999],{"className":985},[638],[579,987],{"className":988,"style":989},[642],"height:0.7335em;vertical-align:-0.1944em;",[579,991,563],{"className":992},[647,648],[579,994],{"className":995,"style":654},[653],[579,997,972],{"className":998},[658],[579,1000],{"className":1001,"style":654},[653],[579,1003,1005,1008,1011],{"className":1004},[638],[579,1006],{"className":1007,"style":668},[642],[579,1009,850],{"className":1010},[647],[579,1012,624],{"className":1013},[647]," sorgt dafür, dass ",[579,1016,1018,1031],{"className":1017},[586],[579,1019,1021],{"className":1020},[590],[592,1022,1023],{"xmlns":594},[597,1024,1025,1029],{},[600,1026,1027],{},[603,1028,605],{},[626,1030,605],{"encoding":628},[579,1032,1034],{"className":1033,"ariaHidden":634},[633],[579,1035,1037,1040],{"className":1036},[638],[579,1038],{"className":1039,"style":643},[642],[579,1041,605],{"className":1042,"style":649},[647,648]," positiv bleibt; mehr als ",[579,1045,1047,1065],{"className":1046},[586],[579,1048,1050],{"className":1049},[590],[592,1051,1052],{"xmlns":594},[597,1053,1054,1062],{},[600,1055,1056,1058,1060],{},[611,1057,624],{},[855,1059,857],{},[603,1061,861],{"mathvariant":860},[626,1063,1064],{"encoding":628},"100\\,\\%",[579,1066,1068],{"className":1067,"ariaHidden":634},[633],[579,1069,1071,1075,1078,1081],{"className":1070},[638],[579,1072],{"className":1073,"style":1074},[642],"height:0.8056em;vertical-align:-0.0556em;",[579,1076,624],{"className":1077},[647],[579,1079],{"className":1080,"style":884},[653],[579,1082,861],{"className":1083},[647]," kann ein Bestand nicht verlieren.",[563,1086,1087,1117,1118,1146,1147,1175,1176,1204],{},[579,1088,1090,1104],{"className":1089},[586],[579,1091,1093],{"className":1092},[590],[592,1094,1095],{"xmlns":594},[597,1096,1097,1102],{},[600,1098,1099],{},[603,1100,1101],{},"t",[626,1103,1101],{"encoding":628},[579,1105,1107],{"className":1106,"ariaHidden":634},[633],[579,1108,1110,1114],{"className":1109},[638],[579,1111],{"className":1112,"style":1113},[642],"height:0.6151em;",[579,1115,1101],{"className":1116},[647,648]," zählt die Zeitschritte in der Einheit, auf die sich ",[579,1119,1121,1134],{"className":1120},[586],[579,1122,1124],{"className":1123},[590],[592,1125,1126],{"xmlns":594},[597,1127,1128,1132],{},[600,1129,1130],{},[603,1131,563],{},[626,1133,563],{"encoding":628},[579,1135,1137],{"className":1136,"ariaHidden":634},[633],[579,1138,1140,1143],{"className":1139},[638],[579,1141],{"className":1142,"style":643},[642],[579,1144,563],{"className":1145},[647,648]," bezieht. Steht ",[579,1148,1150,1163],{"className":1149},[586],[579,1151,1153],{"className":1152},[590],[592,1154,1155],{"xmlns":594},[597,1156,1157,1161],{},[600,1158,1159],{},[603,1160,563],{},[626,1162,563],{"encoding":628},[579,1164,1166],{"className":1165,"ariaHidden":634},[633],[579,1167,1169,1172],{"className":1168},[638],[579,1170],{"className":1171,"style":643},[642],[579,1173,563],{"className":1174},[647,648]," pro Jahr, wird ",[579,1177,1179,1192],{"className":1178},[586],[579,1180,1182],{"className":1181},[590],[592,1183,1184],{"xmlns":594},[597,1185,1186,1190],{},[600,1187,1188],{},[603,1189,1101],{},[626,1191,1101],{"encoding":628},[579,1193,1195],{"className":1194,"ariaHidden":634},[633],[579,1196,1198,1201],{"className":1197},[638],[579,1199],{"className":1200,"style":1113},[642],[579,1202,1101],{"className":1203},[647,648]," in Jahren gemessen.",[558,1206,1208],{"id":1207},"beispiele","Beispiele",[563,1210,1211,1212,1241,1242,1282,1283,1312],{},"Eine Bakterienkultur hat ",[579,1213,1215,1229],{"className":1214},[586],[579,1216,1218],{"className":1217},[590],[592,1219,1220],{"xmlns":594},[597,1221,1222,1227],{},[600,1223,1224],{},[611,1225,1226],{},"500",[626,1228,1226],{"encoding":628},[579,1230,1232],{"className":1231,"ariaHidden":634},[633],[579,1233,1235,1238],{"className":1234},[638],[579,1236],{"className":1237,"style":831},[642],[579,1239,1226],{"className":1240},[647]," Bakterien und wächst um ",[579,1243,1245,1264],{"className":1244},[586],[579,1246,1248],{"className":1247},[590],[592,1249,1250],{"xmlns":594},[597,1251,1252,1261],{},[600,1253,1254,1257,1259],{},[611,1255,1256],{},"20",[855,1258,857],{},[603,1260,861],{"mathvariant":860},[626,1262,1263],{"encoding":628},"20\\,\\%",[579,1265,1267],{"className":1266,"ariaHidden":634},[633],[579,1268,1270,1273,1276,1279],{"className":1269},[638],[579,1271],{"className":1272,"style":1074},[642],[579,1274,1256],{"className":1275},[647],[579,1277],{"className":1278,"style":884},[653],[579,1280,861],{"className":1281},[647]," pro Stunde. Nach ",[579,1284,1286,1300],{"className":1285},[586],[579,1287,1289],{"className":1288},[590],[592,1290,1291],{"xmlns":594},[597,1292,1293,1298],{},[600,1294,1295],{},[611,1296,1297],{},"3",[626,1299,1297],{"encoding":628},[579,1301,1303],{"className":1302,"ariaHidden":634},[633],[579,1304,1306,1309],{"className":1305},[638],[579,1307],{"className":1308,"style":831},[642],[579,1310,1297],{"className":1311},[647]," Stunden:",[579,1314,1316],{"className":1315},[582],[579,1317,1319,1372],{"className":1318},[586],[579,1320,1322],{"className":1321},[590],[592,1323,1324],{"xmlns":594,"display":595},[597,1325,1326,1369],{},[600,1327,1328,1331,1335,1337,1340,1342,1344,1347,1355,1357,1359,1361,1364,1366],{},[603,1329,1330],{},"N",[607,1332,1334],{"stretchy":1333},"false","(",[611,1336,1297],{},[607,1338,1339],{"stretchy":1333},")",[607,1341,609],{},[611,1343,1226],{},[607,1345,1346],{},"⋅",[1348,1349,1350,1353],"msup",{},[611,1351,1352],{},"1,2",[611,1354,1297],{},[607,1356,609],{},[611,1358,1226],{},[607,1360,1346],{},[611,1362,1363],{},"1,728",[607,1365,609],{},[611,1367,1368],{},"864",[626,1370,1371],{"encoding":628},"N(3) = 500 \\cdot 1{,}2^3 = 500 \\cdot 1{,}728 = 864",[579,1373,1375,1404,1422,1485,1503,1531],{"className":1374,"ariaHidden":634},[633],[579,1376,1378,1382,1386,1389,1392,1395,1398,1401],{"className":1377},[638],[579,1379],{"className":1380,"style":1381},[642],"height:1em;vertical-align:-0.25em;",[579,1383,1330],{"className":1384,"style":1385},[647,648],"margin-right:0.109em;",[579,1387,1334],{"className":1388},[696],[579,1390,1297],{"className":1391},[647],[579,1393,1339],{"className":1394},[769],[579,1396],{"className":1397,"style":654},[653],[579,1399,609],{"className":1400},[658],[579,1402],{"className":1403,"style":654},[653],[579,1405,1407,1410,1413,1416,1419],{"className":1406},[638],[579,1408],{"className":1409,"style":831},[642],[579,1411,1226],{"className":1412},[647],[579,1414],{"className":1415,"style":675},[653],[579,1417,1346],{"className":1418},[679],[579,1420],{"className":1421,"style":675},[653],[579,1423,1425,1429,1432,1438,1476,1479,1482],{"className":1424},[638],[579,1426],{"className":1427,"style":1428},[642],"height:1.0585em;vertical-align:-0.1944em;",[579,1430,613],{"className":1431},[647],[579,1433,1435],{"className":1434},[647],[579,1436,950],{"className":1437},[949],[579,1439,1441,1445],{"className":1440},[647],[579,1442,1444],{"className":1443},[647],"2",[579,1446,1449],{"className":1447},[1448],"msupsub",[579,1450,1452],{"className":1451},[704],[579,1453,1455],{"className":1454},[709],[579,1456,1459],{"className":1457,"style":1458},[713],"height:0.8641em;",[579,1460,1462,1466],{"style":1461},"top:-3.113em;margin-right:0.05em;",[579,1463],{"className":1464,"style":1465},[721],"height:2.7em;",[579,1467,1473],{"className":1468},[1469,1470,1471,1472],"sizing","reset-size6","size3","mtight",[579,1474,1297],{"className":1475},[647,1472],[579,1477],{"className":1478,"style":654},[653],[579,1480,609],{"className":1481},[658],[579,1483],{"className":1484,"style":654},[653],[579,1486,1488,1491,1494,1497,1500],{"className":1487},[638],[579,1489],{"className":1490,"style":831},[642],[579,1492,1226],{"className":1493},[647],[579,1495],{"className":1496,"style":675},[653],[579,1498,1346],{"className":1499},[679],[579,1501],{"className":1502,"style":675},[653],[579,1504,1506,1509,1512,1518,1522,1525,1528],{"className":1505},[638],[579,1507],{"className":1508,"style":938},[642],[579,1510,613],{"className":1511},[647],[579,1513,1515],{"className":1514},[647],[579,1516,950],{"className":1517},[949],[579,1519,1521],{"className":1520},[647],"728",[579,1523],{"className":1524,"style":654},[653],[579,1526,609],{"className":1527},[658],[579,1529],{"className":1530,"style":654},[653],[579,1532,1534,1537],{"className":1533},[638],[579,1535],{"className":1536,"style":831},[642],[579,1538,1368],{"className":1539},[647],[563,1541,1542,1543,1583,1584,1623,1624,1653],{},"Ein Auto kostet ",[579,1544,1546,1565],{"className":1545},[586],[579,1547,1549],{"className":1548},[590],[592,1550,1551],{"xmlns":594},[597,1552,1553,1562],{},[600,1554,1555,1557,1559],{},[611,1556,1256],{},[855,1558,857],{},[611,1560,1561],{},"000",[626,1563,1564],{"encoding":628},"20\\,000",[579,1566,1568],{"className":1567,"ariaHidden":634},[633],[579,1569,1571,1574,1577,1580],{"className":1570},[638],[579,1572],{"className":1573,"style":831},[642],[579,1575,1256],{"className":1576},[647],[579,1578],{"className":1579,"style":884},[653],[579,1581,1561],{"className":1582},[647]," € und verliert jedes Jahr ",[579,1585,1587,1605],{"className":1586},[586],[579,1588,1590],{"className":1589},[590],[592,1591,1592],{"xmlns":594},[597,1593,1594,1602],{},[600,1595,1596,1598,1600],{},[611,1597,853],{},[855,1599,857],{},[603,1601,861],{"mathvariant":860},[626,1603,1604],{"encoding":628},"15\\,\\%",[579,1606,1608],{"className":1607,"ariaHidden":634},[633],[579,1609,1611,1614,1617,1620],{"className":1610},[638],[579,1612],{"className":1613,"style":1074},[642],[579,1615,853],{"className":1616},[647],[579,1618],{"className":1619,"style":884},[653],[579,1621,861],{"className":1622},[647]," an Wert. Nach ",[579,1625,1627,1641],{"className":1626},[586],[579,1628,1630],{"className":1629},[590],[592,1631,1632],{"xmlns":594},[597,1633,1634,1639],{},[600,1635,1636],{},[611,1637,1638],{},"4",[626,1640,1638],{"encoding":628},[579,1642,1644],{"className":1643,"ariaHidden":634},[633],[579,1645,1647,1650],{"className":1646},[638],[579,1648],{"className":1649,"style":831},[642],[579,1651,1638],{"className":1652},[647]," Jahren:",[579,1655,1657],{"className":1656},[582],[579,1658,1660,1721],{"className":1659},[586],[579,1661,1663],{"className":1662},[590],[592,1664,1665],{"xmlns":594,"display":595},[597,1666,1667,1718],{},[600,1668,1669,1671,1673,1675,1677,1679,1681,1683,1685,1687,1693,1695,1698,1700,1703,1706,1708,1710,1713,1715],{},[603,1670,1330],{},[607,1672,1334],{"stretchy":1333},[611,1674,1638],{},[607,1676,1339],{"stretchy":1333},[607,1678,609],{},[611,1680,1256],{},[855,1682,857],{},[611,1684,1561],{},[607,1686,1346],{},[1348,1688,1689,1691],{},[611,1690,907],{},[611,1692,1638],{},[607,1694,609],{},[611,1696,1697],{},"10",[855,1699,857],{},[611,1701,1702],{},"440,125",[607,1704,1705],{},"≈",[611,1707,1697],{},[855,1709,857],{},[611,1711,1712],{},"440,13",[855,1714,857],{},[855,1716,1717],{},"Euro",[626,1719,1720],{"encoding":628},"N(4) = 20\\,000 \\cdot 0{,}85^4 = 10\\,440{,}125 \\approx 10\\,440{,}13\\,\\text{Euro}",[579,1722,1724,1751,1775,1833,1868],{"className":1723,"ariaHidden":634},[633],[579,1725,1727,1730,1733,1736,1739,1742,1745,1748],{"className":1726},[638],[579,1728],{"className":1729,"style":1381},[642],[579,1731,1330],{"className":1732,"style":1385},[647,648],[579,1734,1334],{"className":1735},[696],[579,1737,1638],{"className":1738},[647],[579,1740,1339],{"className":1741},[769],[579,1743],{"className":1744,"style":654},[653],[579,1746,609],{"className":1747},[658],[579,1749],{"className":1750,"style":654},[653],[579,1752,1754,1757,1760,1763,1766,1769,1772],{"className":1753},[638],[579,1755],{"className":1756,"style":831},[642],[579,1758,1256],{"className":1759},[647],[579,1761],{"className":1762,"style":884},[653],[579,1764,1561],{"className":1765},[647],[579,1767],{"className":1768,"style":675},[653],[579,1770,1346],{"className":1771},[679],[579,1773],{"className":1774,"style":675},[653],[579,1776,1778,1781,1784,1790,1794,1824,1827,1830],{"className":1777},[638],[579,1779],{"className":1780,"style":1428},[642],[579,1782,942],{"className":1783},[647],[579,1785,1787],{"className":1786},[647],[579,1788,950],{"className":1789},[949],[579,1791,1793],{"className":1792},[647],"8",[579,1795,1797,1801],{"className":1796},[647],[579,1798,1800],{"className":1799},[647],"5",[579,1802,1804],{"className":1803},[1448],[579,1805,1807],{"className":1806},[704],[579,1808,1810],{"className":1809},[709],[579,1811,1813],{"className":1812,"style":1458},[713],[579,1814,1815,1818],{"style":1461},[579,1816],{"className":1817,"style":1465},[721],[579,1819,1821],{"className":1820},[1469,1470,1471,1472],[579,1822,1638],{"className":1823},[647,1472],[579,1825],{"className":1826,"style":654},[653],[579,1828,609],{"className":1829},[658],[579,1831],{"className":1832,"style":654},[653],[579,1834,1836,1839,1842,1845,1849,1855,1859,1862,1865],{"className":1835},[638],[579,1837],{"className":1838,"style":938},[642],[579,1840,1697],{"className":1841},[647],[579,1843],{"className":1844,"style":884},[653],[579,1846,1848],{"className":1847},[647],"440",[579,1850,1852],{"className":1851},[647],[579,1853,950],{"className":1854},[949],[579,1856,1858],{"className":1857},[647],"125",[579,1860],{"className":1861,"style":654},[653],[579,1863,1705],{"className":1864},[658],[579,1866],{"className":1867,"style":654},[653],[579,1869,1871,1875,1878,1881,1884,1890,1894,1897],{"className":1870},[638],[579,1872],{"className":1873,"style":1874},[642],"height:0.8778em;vertical-align:-0.1944em;",[579,1876,1697],{"className":1877},[647],[579,1879],{"className":1880,"style":884},[653],[579,1882,1848],{"className":1883},[647],[579,1885,1887],{"className":1886},[647],[579,1888,950],{"className":1889},[949],[579,1891,1893],{"className":1892},[647],"13",[579,1895],{"className":1896,"style":884},[653],[579,1898,1901],{"className":1899},[647,1900],"text",[579,1902,1717],{"className":1903},[647],[563,1905,1906,1907,1935,1936,2029,2030,2058,2059,2062],{},"Nach wie vielen Stunden hat sich die Bakterienkultur verdoppelt? Gesucht ist ",[579,1908,1910,1923],{"className":1909},[586],[579,1911,1913],{"className":1912},[590],[592,1914,1915],{"xmlns":594},[597,1916,1917,1921],{},[600,1918,1919],{},[603,1920,1101],{},[626,1922,1101],{"encoding":628},[579,1924,1926],{"className":1925,"ariaHidden":634},[633],[579,1927,1929,1932],{"className":1928},[638],[579,1930],{"className":1931,"style":1113},[642],[579,1933,1101],{"className":1934},[647,648]," mit ",[579,1937,1939,1961],{"className":1938},[586],[579,1940,1942],{"className":1941},[590],[592,1943,1944],{"xmlns":594},[597,1945,1946,1958],{},[600,1947,1948,1954,1956],{},[1348,1949,1950,1952],{},[611,1951,1352],{},[603,1953,1101],{},[607,1955,609],{},[611,1957,1444],{},[626,1959,1960],{"encoding":628},"1{,}2^t = 2",[579,1962,1964,2020],{"className":1963,"ariaHidden":634},[633],[579,1965,1967,1971,1974,1980,2011,2014,2017],{"className":1966},[638],[579,1968],{"className":1969,"style":1970},[642],"height:0.988em;vertical-align:-0.1944em;",[579,1972,613],{"className":1973},[647],[579,1975,1977],{"className":1976},[647],[579,1978,950],{"className":1979},[949],[579,1981,1983,1986],{"className":1982},[647],[579,1984,1444],{"className":1985},[647],[579,1987,1989],{"className":1988},[1448],[579,1990,1992],{"className":1991},[704],[579,1993,1995],{"className":1994},[709],[579,1996,1999],{"className":1997,"style":1998},[713],"height:0.7936em;",[579,2000,2002,2005],{"style":2001},"top:-3.063em;margin-right:0.05em;",[579,2003],{"className":2004,"style":1465},[721],[579,2006,2008],{"className":2007},[1469,1470,1471,1472],[579,2009,1101],{"className":2010},[647,648,1472],[579,2012],{"className":2013,"style":654},[653],[579,2015,609],{"className":2016},[658],[579,2018],{"className":2019,"style":654},[653],[579,2021,2023,2026],{"className":2022},[638],[579,2024],{"className":2025,"style":831},[642],[579,2027,1444],{"className":2028},[647],". Weil ",[579,2031,2033,2046],{"className":2032},[586],[579,2034,2036],{"className":2035},[590],[592,2037,2038],{"xmlns":594},[597,2039,2040,2044],{},[600,2041,2042],{},[603,2043,1101],{},[626,2045,1101],{"encoding":628},[579,2047,2049],{"className":2048,"ariaHidden":634},[633],[579,2050,2052,2055],{"className":2051},[638],[579,2053],{"className":2054,"style":1113},[642],[579,2056,1101],{"className":2057},[647,648]," im Exponenten steht, löst man mit dem ",[567,2060,2061],{},"Logarithmus",":",[579,2064,2066],{"className":2065},[582],[579,2067,2069,2105],{"className":2068},[586],[579,2070,2072],{"className":2071},[590],[592,2073,2074],{"xmlns":594,"display":595},[597,2075,2076,2102],{},[600,2077,2078,2080,2082,2095,2097,2099],{},[603,2079,1101],{},[607,2081,609],{},[2083,2084,2085,2093],"msub",{},[600,2086,2087,2090],{},[603,2088,2089],{},"log",[607,2091,2092],{},"⁡",[611,2094,1352],{},[611,2096,1444],{},[607,2098,1705],{},[611,2100,2101],{},"3,8",[626,2103,2104],{"encoding":628},"t = \\log_{1{,}2} 2 \\approx 3{,}8",[579,2106,2108,2126,2209],{"className":2107,"ariaHidden":634},[633],[579,2109,2111,2114,2117,2120,2123],{"className":2110},[638],[579,2112],{"className":2113,"style":1113},[642],[579,2115,1101],{"className":2116},[647,648],[579,2118],{"className":2119,"style":654},[653],[579,2121,609],{"className":2122},[658],[579,2124],{"className":2125,"style":654},[653],[579,2127,2129,2133,2194,2197,2200,2203,2206],{"className":2128},[638],[579,2130],{"className":2131,"style":2132},[642],"height:1.0747em;vertical-align:-0.3802em;",[579,2134,2137,2145],{"className":2135},[2136],"mop",[579,2138,2140,2141],{"className":2139},[2136],"lo",[579,2142,2144],{"style":2143},"margin-right:0.0139em;","g",[579,2146,2148],{"className":2147},[1448],[579,2149,2151,2185],{"className":2150},[704,705],[579,2152,2154,2182],{"className":2153},[709],[579,2155,2158],{"className":2156,"style":2157},[713],"height:0.207em;",[579,2159,2161,2164],{"style":2160},"top:-2.4559em;margin-right:0.05em;",[579,2162],{"className":2163,"style":1465},[721],[579,2165,2167],{"className":2166},[1469,1470,1471,1472],[579,2168,2170,2173,2179],{"className":2169},[647,1472],[579,2171,613],{"className":2172},[647,1472],[579,2174,2176],{"className":2175},[647,1472],[579,2177,950],{"className":2178},[949,1472],[579,2180,1444],{"className":2181},[647,1472],[579,2183,756],{"className":2184},[755],[579,2186,2188],{"className":2187},[709],[579,2189,2192],{"className":2190,"style":2191},[713],"height:0.3802em;",[579,2193],{},[579,2195],{"className":2196,"style":884},[653],[579,2198,1444],{"className":2199},[647],[579,2201],{"className":2202,"style":654},[653],[579,2204,1705],{"className":2205},[658],[579,2207],{"className":2208,"style":654},[653],[579,2210,2212,2215,2218,2224],{"className":2211},[638],[579,2213],{"className":2214,"style":938},[642],[579,2216,1297],{"className":2217},[647],[579,2219,2221],{"className":2220},[647],[579,2222,950],{"className":2223},[949],[579,2225,1793],{"className":2226},[647],[563,2228,2229,2230,2268,2269,2372,2373,2401],{},"Nach etwa ",[579,2231,2233,2247],{"className":2232},[586],[579,2234,2236],{"className":2235},[590],[592,2237,2238],{"xmlns":594},[597,2239,2240,2244],{},[600,2241,2242],{},[611,2243,2101],{},[626,2245,2246],{"encoding":628},"3{,}8",[579,2248,2250],{"className":2249,"ariaHidden":634},[633],[579,2251,2253,2256,2259,2265],{"className":2252},[638],[579,2254],{"className":2255,"style":938},[642],[579,2257,1297],{"className":2258},[647],[579,2260,2262],{"className":2261},[647],[579,2263,950],{"className":2264},[949],[579,2266,1793],{"className":2267},[647]," Stunden. Zur Kontrolle durch Probieren: ",[579,2270,2272,2295],{"className":2271},[586],[579,2273,2275],{"className":2274},[590],[592,2276,2277],{"xmlns":594},[597,2278,2279,2292],{},[600,2280,2281,2287,2289],{},[1348,2282,2283,2285],{},[611,2284,1352],{},[611,2286,1638],{},[607,2288,1705],{},[611,2290,2291],{},"2,07",[626,2293,2294],{"encoding":628},"1{,}2^4 \\approx 2{,}07",[579,2296,2298,2353],{"className":2297,"ariaHidden":634},[633],[579,2299,2301,2305,2308,2314,2344,2347,2350],{"className":2300},[638],[579,2302],{"className":2303,"style":2304},[642],"height:1.0085em;vertical-align:-0.1944em;",[579,2306,613],{"className":2307},[647],[579,2309,2311],{"className":2310},[647],[579,2312,950],{"className":2313},[949],[579,2315,2317,2320],{"className":2316},[647],[579,2318,1444],{"className":2319},[647],[579,2321,2323],{"className":2322},[1448],[579,2324,2326],{"className":2325},[704],[579,2327,2329],{"className":2328},[709],[579,2330,2333],{"className":2331,"style":2332},[713],"height:0.8141em;",[579,2334,2335,2338],{"style":2001},[579,2336],{"className":2337,"style":1465},[721],[579,2339,2341],{"className":2340},[1469,1470,1471,1472],[579,2342,1638],{"className":2343},[647,1472],[579,2345],{"className":2346,"style":654},[653],[579,2348,1705],{"className":2349},[658],[579,2351],{"className":2352,"style":654},[653],[579,2354,2356,2359,2362,2368],{"className":2355},[638],[579,2357],{"className":2358,"style":938},[642],[579,2360,1444],{"className":2361},[647],[579,2363,2365],{"className":2364},[647],[579,2366,950],{"className":2367},[949],[579,2369,2371],{"className":2370},[647],"07",", also knapp unter ",[579,2374,2376,2389],{"className":2375},[586],[579,2377,2379],{"className":2378},[590],[592,2380,2381],{"xmlns":594},[597,2382,2383,2387],{},[600,2384,2385],{},[611,2386,1638],{},[626,2388,1638],{"encoding":628},[579,2390,2392],{"className":2391,"ariaHidden":634},[633],[579,2393,2395,2398],{"className":2394},[638],[579,2396],{"className":2397,"style":831},[642],[579,2399,1638],{"className":2400},[647]," Stunden.",[558,2403,2405],{"id":2404},"typische-fehler","Typische Fehler",[2407,2408,2409,2560,2724,3018],"ul",{},[2410,2411,2412,2413,2451,2452,2490,2491,2519,2520,2559],"li",{},"Den Prozentsatz direkt als Faktor nehmen: Bei ",[579,2414,2416,2433],{"className":2415},[586],[579,2417,2419],{"className":2418},[590],[592,2420,2421],{"xmlns":594},[597,2422,2423,2431],{},[600,2424,2425,2427,2429],{},[611,2426,1256],{},[855,2428,857],{},[603,2430,861],{"mathvariant":860},[626,2432,1263],{"encoding":628},[579,2434,2436],{"className":2435,"ariaHidden":634},[633],[579,2437,2439,2442,2445,2448],{"className":2438},[638],[579,2440],{"className":2441,"style":1074},[642],[579,2443,1256],{"className":2444},[647],[579,2446],{"className":2447,"style":884},[653],[579,2449,861],{"className":2450},[647]," ist der Faktor ",[579,2453,2455,2469],{"className":2454},[586],[579,2456,2458],{"className":2457},[590],[592,2459,2460],{"xmlns":594},[597,2461,2462,2466],{},[600,2463,2464],{},[611,2465,1352],{},[626,2467,2468],{"encoding":628},"1{,}2",[579,2470,2472],{"className":2471,"ariaHidden":634},[633],[579,2473,2475,2478,2481,2487],{"className":2474},[638],[579,2476],{"className":2477,"style":938},[642],[579,2479,613],{"className":2480},[647],[579,2482,2484],{"className":2483},[647],[579,2485,950],{"className":2486},[949],[579,2488,1444],{"className":2489},[647],", nicht ",[579,2492,2494,2507],{"className":2493},[586],[579,2495,2497],{"className":2496},[590],[592,2498,2499],{"xmlns":594},[597,2500,2501,2505],{},[600,2502,2503],{},[611,2504,1256],{},[626,2506,1256],{"encoding":628},[579,2508,2510],{"className":2509,"ariaHidden":634},[633],[579,2511,2513,2516],{"className":2512},[638],[579,2514],{"className":2515,"style":831},[642],[579,2517,1256],{"className":2518},[647]," und nicht ",[579,2521,2523,2538],{"className":2522},[586],[579,2524,2526],{"className":2525},[590],[592,2527,2528],{"xmlns":594},[597,2529,2530,2535],{},[600,2531,2532],{},[611,2533,2534],{},"0,2",[626,2536,2537],{"encoding":628},"0{,}2",[579,2539,2541],{"className":2540,"ariaHidden":634},[633],[579,2542,2544,2547,2550,2556],{"className":2543},[638],[579,2545],{"className":2546,"style":938},[642],[579,2548,942],{"className":2549},[647],[579,2551,2553],{"className":2552},[647],[579,2554,950],{"className":2555},[949],[579,2557,1444],{"className":2558},[647],".",[2410,2561,2562,2563,2606,2607,2646,2647,2490,2685,2559],{},"Bei Abnahme mit dem verlorenen Anteil rechnen: Bei ",[579,2564,2566,2585],{"className":2565},[586],[579,2567,2569],{"className":2568},[590],[592,2570,2571],{"xmlns":594},[597,2572,2573,2583],{},[600,2574,2575,2577,2579,2581],{},[607,2576,850],{},[611,2578,853],{},[855,2580,857],{},[603,2582,861],{"mathvariant":860},[626,2584,864],{"encoding":628},[579,2586,2588],{"className":2587,"ariaHidden":634},[633],[579,2589,2591,2594,2597,2600,2603],{"className":2590},[638],[579,2592],{"className":2593,"style":874},[642],[579,2595,850],{"className":2596},[647],[579,2598,853],{"className":2599},[647],[579,2601],{"className":2602,"style":884},[653],[579,2604,861],{"className":2605},[647]," bleibt ",[579,2608,2610,2628],{"className":2609},[586],[579,2611,2613],{"className":2612},[590],[592,2614,2615],{"xmlns":594},[597,2616,2617,2625],{},[600,2618,2619,2621,2623],{},[611,2620,954],{},[855,2622,857],{},[603,2624,861],{"mathvariant":860},[626,2626,2627],{"encoding":628},"85\\,\\%",[579,2629,2631],{"className":2630,"ariaHidden":634},[633],[579,2632,2634,2637,2640,2643],{"className":2633},[638],[579,2635],{"className":2636,"style":1074},[642],[579,2638,954],{"className":2639},[647],[579,2641],{"className":2642,"style":884},[653],[579,2644,861],{"className":2645},[647]," übrig, der Faktor ist ",[579,2648,2650,2664],{"className":2649},[586],[579,2651,2653],{"className":2652},[590],[592,2654,2655],{"xmlns":594},[597,2656,2657,2661],{},[600,2658,2659],{},[611,2660,907],{},[626,2662,2663],{"encoding":628},"0{,}85",[579,2665,2667],{"className":2666,"ariaHidden":634},[633],[579,2668,2670,2673,2676,2682],{"className":2669},[638],[579,2671],{"className":2672,"style":938},[642],[579,2674,942],{"className":2675},[647],[579,2677,2679],{"className":2678},[647],[579,2680,950],{"className":2681},[949],[579,2683,954],{"className":2684},[647],[579,2686,2688,2703],{"className":2687},[586],[579,2689,2691],{"className":2690},[590],[592,2692,2693],{"xmlns":594},[597,2694,2695,2700],{},[600,2696,2697],{},[611,2698,2699],{},"0,15",[626,2701,2702],{"encoding":628},"0{,}15",[579,2704,2706],{"className":2705,"ariaHidden":634},[633],[579,2707,2709,2712,2715,2721],{"className":2708},[638],[579,2710],{"className":2711,"style":938},[642],[579,2713,942],{"className":2714},[647],[579,2716,2718],{"className":2717},[647],[579,2719,950],{"className":2720},[949],[579,2722,853],{"className":2723},[647],[2410,2725,2726,2727,2765,2766,2794,2795,2823,2824,2852,2853,2949,2950,2978,2979,3017],{},"Linear statt exponentiell rechnen: ",[579,2728,2730,2747],{"className":2729},[586],[579,2731,2733],{"className":2732},[590],[592,2734,2735],{"xmlns":594},[597,2736,2737,2745],{},[600,2738,2739,2741,2743],{},[611,2740,1256],{},[855,2742,857],{},[603,2744,861],{"mathvariant":860},[626,2746,1263],{"encoding":628},[579,2748,2750],{"className":2749,"ariaHidden":634},[633],[579,2751,2753,2756,2759,2762],{"className":2752},[638],[579,2754],{"className":2755,"style":1074},[642],[579,2757,1256],{"className":2758},[647],[579,2760],{"className":2761,"style":884},[653],[579,2763,861],{"className":2764},[647]," von ",[579,2767,2769,2782],{"className":2768},[586],[579,2770,2772],{"className":2771},[590],[592,2773,2774],{"xmlns":594},[597,2775,2776,2780],{},[600,2777,2778],{},[611,2779,1226],{},[626,2781,1226],{"encoding":628},[579,2783,2785],{"className":2784,"ariaHidden":634},[633],[579,2786,2788,2791],{"className":2787},[638],[579,2789],{"className":2790,"style":831},[642],[579,2792,1226],{"className":2793},[647]," sind ",[579,2796,2798,2811],{"className":2797},[586],[579,2799,2801],{"className":2800},[590],[592,2802,2803],{"xmlns":594},[597,2804,2805,2809],{},[600,2806,2807],{},[611,2808,624],{},[626,2810,624],{"encoding":628},[579,2812,2814],{"className":2813,"ariaHidden":634},[633],[579,2815,2817,2820],{"className":2816},[638],[579,2818],{"className":2819,"style":831},[642],[579,2821,624],{"className":2822},[647],", aber nach ",[579,2825,2827,2840],{"className":2826},[586],[579,2828,2830],{"className":2829},[590],[592,2831,2832],{"xmlns":594},[597,2833,2834,2838],{},[600,2835,2836],{},[611,2837,1297],{},[626,2839,1297],{"encoding":628},[579,2841,2843],{"className":2842,"ariaHidden":634},[633],[579,2844,2846,2849],{"className":2845},[638],[579,2847],{"className":2848,"style":831},[642],[579,2850,1297],{"className":2851},[647]," Stunden sind es nicht ",[579,2854,2856,2883],{"className":2855},[586],[579,2857,2859],{"className":2858},[590],[592,2860,2861],{"xmlns":594},[597,2862,2863,2880],{},[600,2864,2865,2867,2869,2871,2873,2875,2877],{},[611,2866,1226],{},[607,2868,616],{},[611,2870,1297],{},[607,2872,1346],{},[611,2874,624],{},[607,2876,609],{},[611,2878,2879],{},"800",[626,2881,2882],{"encoding":628},"500 + 3 \\cdot 100 = 800",[579,2884,2886,2904,2922,2940],{"className":2885,"ariaHidden":634},[633],[579,2887,2889,2892,2895,2898,2901],{"className":2888},[638],[579,2890],{"className":2891,"style":668},[642],[579,2893,1226],{"className":2894},[647],[579,2896],{"className":2897,"style":675},[653],[579,2899,616],{"className":2900},[679],[579,2902],{"className":2903,"style":675},[653],[579,2905,2907,2910,2913,2916,2919],{"className":2906},[638],[579,2908],{"className":2909,"style":831},[642],[579,2911,1297],{"className":2912},[647],[579,2914],{"className":2915,"style":675},[653],[579,2917,1346],{"className":2918},[679],[579,2920],{"className":2921,"style":675},[653],[579,2923,2925,2928,2931,2934,2937],{"className":2924},[638],[579,2926],{"className":2927,"style":831},[642],[579,2929,624],{"className":2930},[647],[579,2932],{"className":2933,"style":654},[653],[579,2935,609],{"className":2936},[658],[579,2938],{"className":2939,"style":654},[653],[579,2941,2943,2946],{"className":2942},[638],[579,2944],{"className":2945,"style":831},[642],[579,2947,2879],{"className":2948},[647],", sondern ",[579,2951,2953,2966],{"className":2952},[586],[579,2954,2956],{"className":2955},[590],[592,2957,2958],{"xmlns":594},[597,2959,2960,2964],{},[600,2961,2962],{},[611,2963,1368],{},[626,2965,1368],{"encoding":628},[579,2967,2969],{"className":2968,"ariaHidden":634},[633],[579,2970,2972,2975],{"className":2971},[638],[579,2973],{"className":2974,"style":831},[642],[579,2976,1368],{"className":2977},[647],", weil die ",[579,2980,2982,2999],{"className":2981},[586],[579,2983,2985],{"className":2984},[590],[592,2986,2987],{"xmlns":594},[597,2988,2989,2997],{},[600,2990,2991,2993,2995],{},[611,2992,1256],{},[855,2994,857],{},[603,2996,861],{"mathvariant":860},[626,2998,1263],{"encoding":628},[579,3000,3002],{"className":3001,"ariaHidden":634},[633],[579,3003,3005,3008,3011,3014],{"className":3004},[638],[579,3006],{"className":3007,"style":1074},[642],[579,3009,1256],{"className":3010},[647],[579,3012],{"className":3013,"style":884},[653],[579,3015,861],{"className":3016},[647]," jede Stunde vom neuen Bestand berechnet werden.",[2410,3019,3020,3021,3065,3066,3110,3111,2559],{},"Annehmen, dass ",[579,3022,3024,3044],{"className":3023},[586],[579,3025,3027],{"className":3026},[590],[592,3028,3029],{"xmlns":594},[597,3030,3031,3041],{},[600,3032,3033,3035,3037,3039],{},[607,3034,616],{},[611,3036,1697],{},[855,3038,857],{},[603,3040,861],{"mathvariant":860},[626,3042,3043],{"encoding":628},"+10\\,\\%",[579,3045,3047],{"className":3046,"ariaHidden":634},[633],[579,3048,3050,3053,3056,3059,3062],{"className":3049},[638],[579,3051],{"className":3052,"style":874},[642],[579,3054,616],{"className":3055},[647],[579,3057,1697],{"className":3058},[647],[579,3060],{"className":3061,"style":884},[653],[579,3063,861],{"className":3064},[647]," und danach ",[579,3067,3069,3089],{"className":3068},[586],[579,3070,3072],{"className":3071},[590],[592,3073,3074],{"xmlns":594},[597,3075,3076,3086],{},[600,3077,3078,3080,3082,3084],{},[607,3079,850],{},[611,3081,1697],{},[855,3083,857],{},[603,3085,861],{"mathvariant":860},[626,3087,3088],{"encoding":628},"-10\\,\\%",[579,3090,3092],{"className":3091,"ariaHidden":634},[633],[579,3093,3095,3098,3101,3104,3107],{"className":3094},[638],[579,3096],{"className":3097,"style":874},[642],[579,3099,850],{"className":3100},[647],[579,3102,1697],{"className":3103},[647],[579,3105],{"className":3106,"style":884},[653],[579,3108,861],{"className":3109},[647]," wieder den Anfangswert ergeben: ",[579,3112,3114,3143],{"className":3113},[586],[579,3115,3117],{"className":3116},[590],[592,3118,3119],{"xmlns":594},[597,3120,3121,3140],{},[600,3122,3123,3125,3127,3130,3132,3135,3137],{},[611,3124,624],{},[607,3126,1346],{},[611,3128,3129],{},"1,1",[607,3131,1346],{},[611,3133,3134],{},"0,9",[607,3136,609],{},[611,3138,3139],{},"99",[626,3141,3142],{"encoding":628},"100 \\cdot 1{,}1 \\cdot 0{,}9 = 99",[579,3144,3146,3164,3191,3219],{"className":3145,"ariaHidden":634},[633],[579,3147,3149,3152,3155,3158,3161],{"className":3148},[638],[579,3150],{"className":3151,"style":831},[642],[579,3153,624],{"className":3154},[647],[579,3156],{"className":3157,"style":675},[653],[579,3159,1346],{"className":3160},[679],[579,3162],{"className":3163,"style":675},[653],[579,3165,3167,3170,3173,3179,3182,3185,3188],{"className":3166},[638],[579,3168],{"className":3169,"style":938},[642],[579,3171,613],{"className":3172},[647],[579,3174,3176],{"className":3175},[647],[579,3177,950],{"className":3178},[949],[579,3180,613],{"className":3181},[647],[579,3183],{"className":3184,"style":675},[653],[579,3186,1346],{"className":3187},[679],[579,3189],{"className":3190,"style":675},[653],[579,3192,3194,3197,3200,3206,3210,3213,3216],{"className":3193},[638],[579,3195],{"className":3196,"style":938},[642],[579,3198,942],{"className":3199},[647],[579,3201,3203],{"className":3202},[647],[579,3204,950],{"className":3205},[949],[579,3207,3209],{"className":3208},[647],"9",[579,3211],{"className":3212,"style":654},[653],[579,3214,609],{"className":3215},[658],[579,3217],{"className":3218,"style":654},[653],[579,3220,3222,3225],{"className":3221},[638],[579,3223],{"className":3224,"style":831},[642],[579,3226,3139],{"className":3227},[647],{"title":3229,"searchDepth":3230,"depth":3230,"links":3231},"",2,[3232,3233,3234],{"id":560,"depth":3230,"text":561},{"id":1207,"depth":3230,"text":1208},{"id":2404,"depth":3230,"text":2405},[3236,3239,3245,3251,3253,3256,3259,3261],{"lhs":3237,"rhs":3238},"N0*(1 + p\u002F100)^(t + 1)","N0*(1 + p\u002F100)^t * (1 + p\u002F100)",{"lhs":3240,"rhs":1368,"where":3241},"N0*(1 + p\u002F100)^t",{"N0":3242,"p":3243,"t":3244},500,20,3,{"lhs":3240,"rhs":3246,"where":3247},"10440.125",{"N0":3248,"p":3249,"t":3250},20000,-15,4,{"lhs":3252,"rhs":1444},"1.2^log(2, 1.2)",{"lhs":3254,"rhs":3255},"round(log(2, 1.2), 1)","3.8",{"lhs":3257,"rhs":3258},"round(1.2^4, 2)","2.07",{"lhs":3260,"rhs":2879},"500 + 3*100",{"lhs":3262,"rhs":3139},"100*1.1*0.9","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p > -100\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">100\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3267,"x":3268,"y":3271,"unit":3274,"unitY":3275,"ticks":3276,"axes":3278,"items":3279},"Graph von N(t) = 500 · 1,2ᵗ, nach 3 Stunden sind es 864 Bakterien",[3269,3270],-1.5,7,[3272,3273],-100,1600,34,0.15,[3277,3242],1,true,[3280,3287,3291,3298,3303],{"type":3281,"from":3282,"to":3284,"style":3286},"segment",[3244,3283],0,[3244,3285],864,"dashed",{"type":3288,"expr":3289,"domain":3290},"function","500*1.2^x",[3283,3270],{"type":3292,"at":3293,"label":3294,"offset":3295},"point",[3283,3242],"N_0",[3296,3297],8,-10,{"type":3292,"at":3299,"label":3300,"offset":3301},[3244,3285],"(3 | 864)",[3302,3297],-62,{"type":3304,"at":3305,"text":1330},"label",[3306,3307],5.6,1350,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 289 255\" width=\"289\" height=\"255\" role=\"img\" aria-label=\"Graph von N(t) = 500 · 1,2ᵗ, nach 3 Stunden sind es 864 Bakterien\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-exponential-growth-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-exponential-growth-clip\">\u003Crect x=\"0\" y=\"0\" width=\"289\" height=\"255\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"240\" x2=\"289\" y2=\"240\" class=\"fig-axis\" marker-end=\"url(#fig-exponential-growth-arrow)\"\u002F>\u003Cline x1=\"51\" y1=\"255\" x2=\"51\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-exponential-growth-arrow)\"\u002F>\u003Cline x1=\"17\" y1=\"237\" x2=\"17\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"20\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">−1\u003C\u002Ftext>\u003Cline x1=\"85\" y1=\"237\" x2=\"85\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"88\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">1\u003C\u002Ftext>\u003Cline x1=\"119\" y1=\"237\" x2=\"119\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"122\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">2\u003C\u002Ftext>\u003Cline x1=\"153\" y1=\"237\" x2=\"153\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"156\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">3\u003C\u002Ftext>\u003Cline x1=\"187\" y1=\"237\" x2=\"187\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"190\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">4\u003C\u002Ftext>\u003Cline x1=\"221\" y1=\"237\" x2=\"221\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"224\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">5\u003C\u002Ftext>\u003Cline x1=\"255\" y1=\"237\" x2=\"255\" y2=\"243\" class=\"fig-axis\"\u002F>\u003Ctext x=\"258\" y=\"254\" text-anchor=\"start\" class=\"fig-tick\">6\u003C\u002Ftext>\u003Cline x1=\"48\" y1=\"165\" x2=\"54\" y2=\"165\" class=\"fig-axis\"\u002F>\u003Ctext x=\"45\" y=\"158\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">500\u003C\u002Ftext>\u003Cline x1=\"48\" y1=\"90\" x2=\"54\" y2=\"90\" class=\"fig-axis\"\u002F>\u003Ctext x=\"45\" y=\"83\" text-anchor=\"end\" dominant-baseline=\"middle\" class=\"fig-tick\">1000\u003C\u002Ftext>\u003Ctext x=\"283\" y=\"228\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">x\u003C\u002Ftext>\u003Ctext x=\"63\" y=\"8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y\u003C\u002Ftext>\u003Cline x1=\"153\" y1=\"240\" x2=\"153\" y2=\"110.4\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 51 165 L 51.99 164.6 L 52.98 164.2 L 53.97 163.79 L 54.97 163.39 L 55.96 162.98 L 56.95 162.57 L 57.94 162.16 L 58.93 161.74 L 59.93 161.32 L 60.92 160.9 L 61.91 160.48 L 62.9 160.06 L 63.89 159.63 L 64.88 159.2 L 65.88 158.77 L 66.87 158.34 L 67.86 157.9 L 68.85 157.47 L 69.84 157.03 L 70.83 156.58 L 71.82 156.14 L 72.82 155.69 L 73.81 155.24 L 74.8 154.79 L 75.79 154.34 L 76.78 153.88 L 77.78 153.42 L 78.77 152.96 L 79.76 152.49 L 80.75 152.03 L 81.74 151.56 L 82.73 151.09 L 83.73 150.61 L 84.72 150.14 L 85.71 149.66 L 86.7 149.18 L 87.69 148.69 L 88.68 148.2 L 89.68 147.72 L 90.67 147.22 L 91.66 146.73 L 92.65 146.23 L 93.64 145.73 L 94.63 145.23 L 95.63 144.72 L 96.62 144.22 L 97.61 143.7 L 98.6 143.19 L 99.59 142.67 L 100.58 142.16 L 101.57 141.63 L 102.57 141.11 L 103.56 140.58 L 104.55 140.05 L 105.54 139.52 L 106.53 138.98 L 107.53 138.45 L 108.52 137.9 L 109.51 137.36 L 110.5 136.81 L 111.49 136.26 L 112.48 135.71 L 113.48 135.15 L 114.47 134.59 L 115.46 134.03 L 116.45 133.47 L 117.44 132.9 L 118.43 132.33 L 119.43 131.75 L 120.42 131.18 L 121.41 130.6 L 122.4 130.01 L 123.39 129.43 L 124.38 128.84 L 125.38 128.24 L 126.37 127.65 L 127.36 127.05 L 128.35 126.45 L 129.34 125.84 L 130.33 125.23 L 131.32 124.62 L 132.32 124.01 L 133.31 123.39 L 134.3 122.77 L 135.29 122.14 L 136.28 121.51 L 137.27 120.88 L 138.27 120.25 L 139.26 119.61 L 140.25 118.96 L 141.24 118.32 L 142.23 117.67 L 143.23 117.02 L 144.22 116.36 L 145.21 115.7 L 146.2 115.04 L 147.19 114.37 L 148.18 113.7 L 149.18 113.03 L 150.17 112.35 L 151.16 111.67 L 152.15 110.99 L 153.14 110.3 L 154.13 109.61 L 155.13 108.91 L 156.12 108.22 L 157.11 107.51 L 158.1 106.81 L 159.09 106.1 L 160.08 105.38 L 161.07 104.66 L 162.07 103.94 L 163.06 103.22 L 164.05 102.49 L 165.04 101.76 L 166.03 101.02 L 167.02 100.28 L 168.02 99.53 L 169.01 98.78 L 170 98.03 L 170.99 97.27 L 171.98 96.51 L 172.98 95.75 L 173.97 94.98 L 174.96 94.2 L 175.95 93.43 L 176.94 92.65 L 177.93 91.86 L 178.93 91.07 L 179.92 90.28 L 180.91 89.48 L 181.9 88.68 L 182.89 87.87 L 183.88 87.06 L 184.88 86.24 L 185.87 85.42 L 186.86 84.6 L 187.85 83.77 L 188.84 82.94 L 189.83 82.1 L 190.83 81.26 L 191.82 80.41 L 192.81 79.56 L 193.8 78.7 L 194.79 77.84 L 195.78 76.98 L 196.77 76.11 L 197.77 75.24 L 198.76 74.36 L 199.75 73.48 L 200.74 72.59 L 201.73 71.69 L 202.73 70.8 L 203.72 69.9 L 204.71 68.99 L 205.7 68.08 L 206.69 67.16 L 207.68 66.24 L 208.68 65.31 L 209.67 64.38 L 210.66 63.44 L 211.65 62.5 L 212.64 61.56 L 213.63 60.6 L 214.63 59.65 L 215.62 58.69 L 216.61 57.72 L 217.6 56.75 L 218.59 55.77 L 219.58 54.79 L 220.58 53.8 L 221.57 52.81 L 222.56 51.81 L 223.55 50.81 L 224.54 49.8 L 225.53 48.78 L 226.52 47.76 L 227.52 46.74 L 228.51 45.71 L 229.5 44.67 L 230.49 43.63 L 231.48 42.58 L 232.48 41.53 L 233.47 40.47 L 234.46 39.41 L 235.45 38.34 L 236.44 37.26 L 237.43 36.18 L 238.43 35.1 L 239.42 34 L 240.41 32.91 L 241.4 31.8 L 242.39 30.69 L 243.38 29.58 L 244.38 28.45 L 245.37 27.33 L 246.36 26.19 L 247.35 25.05 L 248.34 23.91 L 249.33 22.75 L 250.33 21.6 L 251.32 20.43 L 252.31 19.26 L 253.3 18.08 L 254.29 16.9 L 255.28 15.71 L 256.27 14.51 L 257.27 13.31 L 258.26 12.1 L 259.25 10.89 L 260.24 9.67 L 261.23 8.44 L 262.23 7.2 L 263.22 5.96 L 264.21 4.72 L 265.2 3.46 L 266.19 2.2 L 267.18 0.93 L 268.18 -0.34 L 269.17 -1.62 L 270.16 -2.91 L 271.15 -4.21 L 272.14 -5.51 L 273.13 -6.82 L 274.13 -8.14 L 275.12 -9.46 L 276.11 -10.79 L 277.1 -12.13 L 278.09 -13.47 L 279.08 -14.82 L 280.08 -16.18 L 281.07 -17.55 L 282.06 -18.92 L 283.05 -20.3 L 284.04 -21.69 L 285.03 -23.08 L 286.02 -24.49 L 287.02 -25.9 L 288.01 -27.31 L 289 -28.74\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-exponential-growth-clip)\"\u002F>\u003Ccircle cx=\"51\" cy=\"165\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"59\" y=\"155\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">N\u003Ctspan class=\"fig-sub\" dy=\"4\">0\u003C\u002Ftspan>\u003C\u002Ftext>\u003Ccircle cx=\"153\" cy=\"110.4\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"91\" y=\"100.4\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">(3 | 864)\u003C\u002Ftext>\u003Ctext x=\"241.4\" y=\"37.5\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">N\u003C\u002Ftext>\u003C\u002Fsvg>","exponential-growth","N(t) = N_0 \\cdot \\left(1 + \\frac{p}{100}\\right)^t","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>N\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N(t) = N_0 \\cdot \\left(1 + \\frac{p}{100}\\right)^t\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0195em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">100\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3335em;\">\u003Cspan style=\"top:-3.6029em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum",[],[3317,3318,3319,3320],"exponential-decay","doubling-time","half-life","exponential-ode",{"title":548,"description":3229},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum","Wächst oder schrumpft ein Bestand pro Schritt um p %, ist er nach t Schritten N₀ · (1 + p\u002F100)ᵗ.",[3325,3326,3327,3328],"exponentielles wachstum","exponentielle abnahme","prozent","wachstumsfaktor",[3330,3334,3337,3340],{"symbol":3331,"meaning":3332,"symbolHtml":3333},"N(t)","Bestand nach t Zeitschritten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>N\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N(t)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3294,"meaning":3335,"symbolHtml":3336},"Anfangsbestand zum Zeitpunkt t = 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":563,"meaning":3338,"symbolHtml":3339},"prozentuale Änderung pro Zeitschritt (bei Abnahme negativ)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1101,"meaning":3341,"symbolHtml":3342},"Anzahl der Zeitschritte (z.B. Stunden oder Jahre)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">t\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","TGzq0BWAXapIO6F02oetoeOy3gO52IjKsvcl3Yw1okI",[3345,3348,3351,3354],{"stem":3346,"title":3347,"category":172},"de\u002Fformulas\u002Fmath\u002Fdifferential-equations\u002Fdgl-exponentielles-wachstum","DGL des exponentiellen Wachstums",{"stem":3349,"title":3350,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielle-abnahme","Exponentielle Abnahme",{"stem":3352,"title":3353,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fhalbwertszeit","Halbwertszeit",{"stem":3355,"title":3356,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fverdopplungszeit","Verdopplungszeit",1793824274293]