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",[579,1057,1059,1073],{"className":1058},[586],[579,1060,1062],{"className":1061},[590],[592,1063,1064],{"xmlns":594},[597,1065,1066,1071],{},[600,1067,1068],{},[611,1069,1070],{},"3",[626,1072,1070],{"encoding":628},[579,1074,1076],{"className":1075,"ariaHidden":634},[633],[579,1077,1079,1082],{"className":1078},[638],[579,1080],{"className":1081,"style":956},[642],[579,1083,1070],{"className":1084},[647]," Stunden noch",[579,1087,1089],{"className":1088},[582],[579,1090,1092,1154],{"className":1091},[586],[579,1093,1095],{"className":1094},[590],[592,1096,1097],{"xmlns":594,"display":595},[597,1098,1099,1151],{},[600,1100,1101,1104,1108,1110,1113,1115,1117,1120,1127,1129,1131,1133,1136,1138,1141,1144,1147,1149],{},[603,1102,1103],{},"N",[607,1105,1107],{"stretchy":1106},"false","(",[611,1109,1070],{},[607,1111,1112],{"stretchy":1106},")",[607,1114,609],{},[611,1116,1024],{},[607,1118,1119],{},"⋅",[1121,1122,1123,1125],"msup",{},[611,1124,838],{},[611,1126,1070],{},[607,1128,609],{},[611,1130,1024],{},[607,1132,1119],{},[611,1134,1135],{},"0,421875",[607,1137,609],{},[611,1139,1140],{},"84,375",[607,1142,1143],{},"≈",[611,1145,1146],{},"84,4",[789,1148,791],{},[789,1150,1029],{},[626,1152,1153],{"encoding":628},"N(3) = 200 \\cdot 0{,}75^3 = 200 \\cdot 0{,}421875 = 84{,}375 \\approx 84{,}4\\,\\text{mg}",[579,1155,1157,1186,1204,1271,1289,1317,1346],{"className":1156,"ariaHidden":634},[633],[579,1158,1160,1164,1168,1171,1174,1177,1180,1183],{"className":1159},[638],[579,1161],{"className":1162,"style":1163},[642],"height:1em;vertical-align:-0.25em;",[579,1165,1103],{"className":1166,"style":1167},[647,648],"margin-right:0.109em;",[579,1169,1107],{"className":1170},[696],[579,1172,1070],{"className":1173},[647],[579,1175,1112],{"className":1176},[769],[579,1178],{"className":1179,"style":654},[653],[579,1181,609],{"className":1182},[658],[579,1184],{"className":1185,"style":654},[653],[579,1187,1189,1192,1195,1198,1201],{"className":1188},[638],[579,1190],{"className":1191,"style":956},[642],[579,1193,1024],{"className":1194},[647],[579,1196],{"className":1197,"style":675},[653],[579,1199,1119],{"className":1200},[679],[579,1202],{"className":1203,"style":675},[653],[579,1205,1207,1211,1214,1220,1224,1262,1265,1268],{"className":1206},[638],[579,1208],{"className":1209,"style":1210},[642],"height:1.0585em;vertical-align:-0.1944em;",[579,1212,873],{"className":1213},[647],[579,1215,1217],{"className":1216},[647],[579,1218,881],{"className":1219},[880],[579,1221,1223],{"className":1222},[647],"7",[579,1225,1227,1231],{"className":1226},[647],[579,1228,1230],{"className":1229},[647],"5",[579,1232,1235],{"className":1233},[1234],"msupsub",[579,1236,1238],{"className":1237},[704],[579,1239,1241],{"className":1240},[709],[579,1242,1245],{"className":1243,"style":1244},[713],"height:0.8641em;",[579,1246,1248,1252],{"style":1247},"top:-3.113em;margin-right:0.05em;",[579,1249],{"className":1250,"style":1251},[721],"height:2.7em;",[579,1253,1259],{"className":1254},[1255,1256,1257,1258],"sizing","reset-size6","size3","mtight",[579,1260,1070],{"className":1261},[647,1258],[579,1263],{"className":1264,"style":654},[653],[579,1266,609],{"className":1267},[658],[579,1269],{"className":1270,"style":654},[653],[579,1272,1274,1277,1280,1283,1286],{"className":1273},[638],[579,1275],{"className":1276,"style":956},[642],[579,1278,1024],{"className":1279},[647],[579,1281],{"className":1282,"style":675},[653],[579,1284,1119],{"className":1285},[679],[579,1287],{"className":1288,"style":675},[653],[579,1290,1292,1295,1298,1304,1308,1311,1314],{"className":1291},[638],[579,1293],{"className":1294,"style":869},[642],[579,1296,873],{"className":1297},[647],[579,1299,1301],{"className":1300},[647],[579,1302,881],{"className":1303},[880],[579,1305,1307],{"className":1306},[647],"421875",[579,1309],{"className":1310,"style":654},[653],[579,1312,609],{"className":1313},[658],[579,1315],{"className":1316,"style":654},[653],[579,1318,1320,1323,1327,1333,1337,1340,1343],{"className":1319},[638],[579,1321],{"className":1322,"style":869},[642],[579,1324,1326],{"className":1325},[647],"84",[579,1328,1330],{"className":1329},[647],[579,1331,881],{"className":1332},[880],[579,1334,1336],{"className":1335},[647],"375",[579,1338],{"className":1339,"style":654},[653],[579,1341,1143],{"className":1342},[658],[579,1344],{"className":1345,"style":654},[653],[579,1347,1349,1352,1355,1361,1365,1368],{"className":1348},[638],[579,1350],{"className":1351,"style":869},[642],[579,1353,1326],{"className":1354},[647],[579,1356,1358],{"className":1357},[647],[579,1359,881],{"className":1360},[880],[579,1362,1364],{"className":1363},[647],"4",[579,1366],{"className":1367,"style":815},[653],[579,1369,1371],{"className":1370},[647,1051],[579,1372,1029],{"className":1373},[647],[564,1375,1376],{},"vorhanden.",[564,1378,1379,1380,1409,1410,1450,1451,1479],{},"Ein Tierbestand von ",[579,1381,1383,1397],{"className":1382},[586],[579,1384,1386],{"className":1385},[590],[592,1387,1388],{"xmlns":594},[597,1389,1390,1395],{},[600,1391,1392],{},[611,1393,1394],{},"1500",[626,1396,1394],{"encoding":628},[579,1398,1400],{"className":1399,"ariaHidden":634},[633],[579,1401,1403,1406],{"className":1402},[638],[579,1404],{"className":1405,"style":956},[642],[579,1407,1394],{"className":1408},[647]," Tieren schrumpft jedes Jahr um ",[579,1411,1413,1432],{"className":1412},[586],[579,1414,1416],{"className":1415},[590],[592,1417,1418],{"xmlns":594},[597,1419,1420,1429],{},[600,1421,1422,1425,1427],{},[611,1423,1424],{},"8",[789,1426,791],{},[603,1428,795],{"mathvariant":794},[626,1430,1431],{"encoding":628},"8\\,\\%",[579,1433,1435],{"className":1434,"ariaHidden":634},[633],[579,1436,1438,1441,1444,1447],{"className":1437},[638],[579,1439],{"className":1440,"style":808},[642],[579,1442,1424],{"className":1443},[647],[579,1445],{"className":1446,"style":815},[653],[579,1448,795],{"className":1449},[647],". Nach ",[579,1452,1454,1467],{"className":1453},[586],[579,1455,1457],{"className":1456},[590],[592,1458,1459],{"xmlns":594},[597,1460,1461,1465],{},[600,1462,1463],{},[611,1464,1230],{},[626,1466,1230],{"encoding":628},[579,1468,1470],{"className":1469,"ariaHidden":634},[633],[579,1471,1473,1476],{"className":1472},[638],[579,1474],{"className":1475,"style":956},[642],[579,1477,1230],{"className":1478},[647]," Jahren:",[579,1481,1483],{"className":1482},[582],[579,1484,1486,1533],{"className":1485},[586],[579,1487,1489],{"className":1488},[590],[592,1490,1491],{"xmlns":594,"display":595},[597,1492,1493,1530],{},[600,1494,1495,1497,1499,1501,1503,1505,1507,1509,1516,1518,1520,1522,1525,1527],{},[603,1496,1103],{},[607,1498,1107],{"stretchy":1106},[611,1500,1230],{},[607,1502,1112],{"stretchy":1106},[607,1504,609],{},[611,1506,1394],{},[607,1508,1119],{},[1121,1510,1511,1514],{},[611,1512,1513],{},"0,92",[611,1515,1230],{},[607,1517,1143],{},[611,1519,1394],{},[607,1521,1119],{},[611,1523,1524],{},"0,6591",[607,1526,1143],{},[611,1528,1529],{},"989",[626,1531,1532],{"encoding":628},"N(5) = 1500 \\cdot 0{,}92^5 \\approx 1500 \\cdot 0{,}6591 \\approx 989",[579,1534,1536,1563,1581,1639,1657,1685],{"className":1535,"ariaHidden":634},[633],[579,1537,1539,1542,1545,1548,1551,1554,1557,1560],{"className":1538},[638],[579,1540],{"className":1541,"style":1163},[642],[579,1543,1103],{"className":1544,"style":1167},[647,648],[579,1546,1107],{"className":1547},[696],[579,1549,1230],{"className":1550},[647],[579,1552,1112],{"className":1553},[769],[579,1555],{"className":1556,"style":654},[653],[579,1558,609],{"className":1559},[658],[579,1561],{"className":1562,"style":654},[653],[579,1564,1566,1569,1572,1575,1578],{"className":1565},[638],[579,1567],{"className":1568,"style":956},[642],[579,1570,1394],{"className":1571},[647],[579,1573],{"className":1574,"style":675},[653],[579,1576,1119],{"className":1577},[679],[579,1579],{"className":1580,"style":675},[653],[579,1582,1584,1587,1590,1596,1600,1630,1633,1636],{"className":1583},[638],[579,1585],{"className":1586,"style":1210},[642],[579,1588,873],{"className":1589},[647],[579,1591,1593],{"className":1592},[647],[579,1594,881],{"className":1595},[880],[579,1597,1599],{"className":1598},[647],"9",[579,1601,1603,1607],{"className":1602},[647],[579,1604,1606],{"className":1605},[647],"2",[579,1608,1610],{"className":1609},[1234],[579,1611,1613],{"className":1612},[704],[579,1614,1616],{"className":1615},[709],[579,1617,1619],{"className":1618,"style":1244},[713],[579,1620,1621,1624],{"style":1247},[579,1622],{"className":1623,"style":1251},[721],[579,1625,1627],{"className":1626},[1255,1256,1257,1258],[579,1628,1230],{"className":1629},[647,1258],[579,1631],{"className":1632,"style":654},[653],[579,1634,1143],{"className":1635},[658],[579,1637],{"className":1638,"style":654},[653],[579,1640,1642,1645,1648,1651,1654],{"className":1641},[638],[579,1643],{"className":1644,"style":956},[642],[579,1646,1394],{"className":1647},[647],[579,1649],{"className":1650,"style":675},[653],[579,1652,1119],{"className":1653},[679],[579,1655],{"className":1656,"style":675},[653],[579,1658,1660,1663,1666,1672,1676,1679,1682],{"className":1659},[638],[579,1661],{"className":1662,"style":869},[642],[579,1664,873],{"className":1665},[647],[579,1667,1669],{"className":1668},[647],[579,1670,881],{"className":1671},[880],[579,1673,1675],{"className":1674},[647],"6591",[579,1677],{"className":1678,"style":654},[653],[579,1680,1143],{"className":1681},[658],[579,1683],{"className":1684,"style":654},[653],[579,1686,1688,1691],{"className":1687},[638],[579,1689],{"className":1690,"style":956},[642],[579,1692,1529],{"className":1693},[647],[564,1695,1696,1697,1727,1728,1834],{},"Wann ist beim Medikament nur noch die Hälfte da? Gesucht ist ",[579,1698,1700,1714],{"className":1699},[586],[579,1701,1703],{"className":1702},[590],[592,1704,1705],{"xmlns":594},[597,1706,1707,1712],{},[600,1708,1709],{},[603,1710,1711],{},"t",[626,1713,1711],{"encoding":628},[579,1715,1717],{"className":1716,"ariaHidden":634},[633],[579,1718,1720,1724],{"className":1719},[638],[579,1721],{"className":1722,"style":1723},[642],"height:0.6151em;",[579,1725,1711],{"className":1726},[647,648]," mit ",[579,1729,1731,1754],{"className":1730},[586],[579,1732,1734],{"className":1733},[590],[592,1735,1736],{"xmlns":594},[597,1737,1738,1751],{},[600,1739,1740,1746,1748],{},[1121,1741,1742,1744],{},[611,1743,838],{},[603,1745,1711],{},[607,1747,609],{},[611,1749,1750],{},"0,5",[626,1752,1753],{"encoding":628},"0{,}75^t = 0{,}5",[579,1755,1757,1816],{"className":1756,"ariaHidden":634},[633],[579,1758,1760,1764,1767,1773,1776,1807,1810,1813],{"className":1759},[638],[579,1761],{"className":1762,"style":1763},[642],"height:0.988em;vertical-align:-0.1944em;",[579,1765,873],{"className":1766},[647],[579,1768,1770],{"className":1769},[647],[579,1771,881],{"className":1772},[880],[579,1774,1223],{"className":1775},[647],[579,1777,1779,1782],{"className":1778},[647],[579,1780,1230],{"className":1781},[647],[579,1783,1785],{"className":1784},[1234],[579,1786,1788],{"className":1787},[704],[579,1789,1791],{"className":1790},[709],[579,1792,1795],{"className":1793,"style":1794},[713],"height:0.7936em;",[579,1796,1798,1801],{"style":1797},"top:-3.063em;margin-right:0.05em;",[579,1799],{"className":1800,"style":1251},[721],[579,1802,1804],{"className":1803},[1255,1256,1257,1258],[579,1805,1711],{"className":1806},[647,648,1258],[579,1808],{"className":1809,"style":654},[653],[579,1811,609],{"className":1812},[658],[579,1814],{"className":1815,"style":654},[653],[579,1817,1819,1822,1825,1831],{"className":1818},[638],[579,1820],{"className":1821,"style":869},[642],[579,1823,873],{"className":1824},[647],[579,1826,1828],{"className":1827},[647],[579,1829,881],{"className":1830},[880],[579,1832,1230],{"className":1833},[647],":",[579,1836,1838],{"className":1837},[582],[579,1839,1841,1877],{"className":1840},[586],[579,1842,1844],{"className":1843},[590],[592,1845,1846],{"xmlns":594,"display":595},[597,1847,1848,1874],{},[600,1849,1850,1852,1854,1867,1869,1871],{},[603,1851,1711],{},[607,1853,609],{},[1855,1856,1857,1865],"msub",{},[600,1858,1859,1862],{},[603,1860,1861],{},"log",[607,1863,1864],{},"⁡",[611,1866,838],{},[611,1868,1750],{},[607,1870,1143],{},[611,1872,1873],{},"2,41",[626,1875,1876],{"encoding":628},"t = \\log_{0{,}75} 0{,}5 \\approx 2{,}41",[579,1878,1880,1898,1990],{"className":1879,"ariaHidden":634},[633],[579,1881,1883,1886,1889,1892,1895],{"className":1882},[638],[579,1884],{"className":1885,"style":1723},[642],[579,1887,1711],{"className":1888},[647,648],[579,1890],{"className":1891,"style":654},[653],[579,1893,609],{"className":1894},[658],[579,1896],{"className":1897,"style":654},[653],[579,1899,1901,1905,1966,1969,1972,1978,1981,1984,1987],{"className":1900},[638],[579,1902],{"className":1903,"style":1904},[642],"height:1.0747em;vertical-align:-0.3802em;",[579,1906,1909,1917],{"className":1907},[1908],"mop",[579,1910,1912,1913],{"className":1911},[1908],"lo",[579,1914,1916],{"style":1915},"margin-right:0.0139em;","g",[579,1918,1920],{"className":1919},[1234],[579,1921,1923,1957],{"className":1922},[704,705],[579,1924,1926,1954],{"className":1925},[709],[579,1927,1930],{"className":1928,"style":1929},[713],"height:0.207em;",[579,1931,1933,1936],{"style":1932},"top:-2.4559em;margin-right:0.05em;",[579,1934],{"className":1935,"style":1251},[721],[579,1937,1939],{"className":1938},[1255,1256,1257,1258],[579,1940,1942,1945,1951],{"className":1941},[647,1258],[579,1943,873],{"className":1944},[647,1258],[579,1946,1948],{"className":1947},[647,1258],[579,1949,881],{"className":1950},[880,1258],[579,1952,885],{"className":1953},[647,1258],[579,1955,756],{"className":1956},[755],[579,1958,1960],{"className":1959},[709],[579,1961,1964],{"className":1962,"style":1963},[713],"height:0.3802em;",[579,1965],{},[579,1967],{"className":1968,"style":815},[653],[579,1970,873],{"className":1971},[647],[579,1973,1975],{"className":1974},[647],[579,1976,881],{"className":1977},[880],[579,1979,1230],{"className":1980},[647],[579,1982],{"className":1983,"style":654},[653],[579,1985,1143],{"className":1986},[658],[579,1988],{"className":1989,"style":654},[653],[579,1991,1993,1996,1999,2005],{"className":1992},[638],[579,1994],{"className":1995,"style":869},[642],[579,1997,1606],{"className":1998},[647],[579,2000,2002],{"className":2001},[647],[579,2003,881],{"className":2004},[880],[579,2006,2008],{"className":2007},[647],"41",[564,2010,2011,2012,2051],{},"Nach etwa ",[579,2013,2015,2030],{"className":2014},[586],[579,2016,2018],{"className":2017},[590],[592,2019,2020],{"xmlns":594},[597,2021,2022,2027],{},[600,2023,2024],{},[611,2025,2026],{},"2,4",[626,2028,2029],{"encoding":628},"2{,}4",[579,2031,2033],{"className":2032,"ariaHidden":634},[633],[579,2034,2036,2039,2042,2048],{"className":2035},[638],[579,2037],{"className":2038,"style":869},[642],[579,2040,1606],{"className":2041},[647],[579,2043,2045],{"className":2044},[647],[579,2046,881],{"className":2047},[880],[579,2049,1364],{"className":2050},[647]," Stunden.",[559,2053,2055],{"id":2054},"typische-fehler","Typische Fehler",[2057,2058,2059,2271,2586],"ul",{},[2060,2061,2062,2063,2192,2193,2231,2232,2270],"li",{},"Mit dem abgebauten Anteil statt mit dem Rest rechnen: ",[579,2064,2066,2094],{"className":2065},[586],[579,2067,2069],{"className":2068},[590],[592,2070,2071],{"xmlns":594},[597,2072,2073,2091],{},[600,2074,2075,2077,2079,2086,2088],{},[611,2076,1024],{},[607,2078,1119],{},[1121,2080,2081,2084],{},[611,2082,2083],{},"0,25",[611,2085,1070],{},[607,2087,609],{},[611,2089,2090],{},"3,125",[626,2092,2093],{"encoding":628},"200 \\cdot 0{,}25^3 = 3{,}125",[579,2095,2097,2115,2173],{"className":2096,"ariaHidden":634},[633],[579,2098,2100,2103,2106,2109,2112],{"className":2099},[638],[579,2101],{"className":2102,"style":956},[642],[579,2104,1024],{"className":2105},[647],[579,2107],{"className":2108,"style":675},[653],[579,2110,1119],{"className":2111},[679],[579,2113],{"className":2114,"style":675},[653],[579,2116,2118,2122,2125,2131,2134,2164,2167,2170],{"className":2117},[638],[579,2119],{"className":2120,"style":2121},[642],"height:1.0085em;vertical-align:-0.1944em;",[579,2123,873],{"className":2124},[647],[579,2126,2128],{"className":2127},[647],[579,2129,881],{"className":2130},[880],[579,2132,1606],{"className":2133},[647],[579,2135,2137,2140],{"className":2136},[647],[579,2138,1230],{"className":2139},[647],[579,2141,2143],{"className":2142},[1234],[579,2144,2146],{"className":2145},[704],[579,2147,2149],{"className":2148},[709],[579,2150,2153],{"className":2151,"style":2152},[713],"height:0.8141em;",[579,2154,2155,2158],{"style":1797},[579,2156],{"className":2157,"style":1251},[721],[579,2159,2161],{"className":2160},[1255,1256,1257,1258],[579,2162,1070],{"className":2163},[647,1258],[579,2165],{"className":2166,"style":654},[653],[579,2168,609],{"className":2169},[658],[579,2171],{"className":2172,"style":654},[653],[579,2174,2176,2179,2182,2188],{"className":2175},[638],[579,2177],{"className":2178,"style":869},[642],[579,2180,1070],{"className":2181},[647],[579,2183,2185],{"className":2184},[647],[579,2186,881],{"className":2187},[880],[579,2189,2191],{"className":2190},[647],"125"," ist falsch. Der Faktor ist ",[579,2194,2196,2210],{"className":2195},[586],[579,2197,2199],{"className":2198},[590],[592,2200,2201],{"xmlns":594},[597,2202,2203,2207],{},[600,2204,2205],{},[611,2206,838],{},[626,2208,2209],{"encoding":628},"0{,}75",[579,2211,2213],{"className":2212,"ariaHidden":634},[633],[579,2214,2216,2219,2222,2228],{"className":2215},[638],[579,2217],{"className":2218,"style":869},[642],[579,2220,873],{"className":2221},[647],[579,2223,2225],{"className":2224},[647],[579,2226,881],{"className":2227},[880],[579,2229,885],{"className":2230},[647],", nicht ",[579,2233,2235,2249],{"className":2234},[586],[579,2236,2238],{"className":2237},[590],[592,2239,2240],{"xmlns":594},[597,2241,2242,2246],{},[600,2243,2244],{},[611,2245,2083],{},[626,2247,2248],{"encoding":628},"0{,}25",[579,2250,2252],{"className":2251,"ariaHidden":634},[633],[579,2253,2255,2258,2261,2267],{"className":2254},[638],[579,2256],{"className":2257,"style":869},[642],[579,2259,873],{"className":2260},[647],[579,2262,2264],{"className":2263},[647],[579,2265,881],{"className":2266},[880],[579,2268,787],{"className":2269},[647],".",[2060,2272,2273,2274,2302,2303,2396,2397,2493,2494,2534,2535,2270],{},"Die Prozente einfach addieren: Nach ",[579,2275,2277,2290],{"className":2276},[586],[579,2278,2280],{"className":2279},[590],[592,2281,2282],{"xmlns":594},[597,2283,2284,2288],{},[600,2285,2286],{},[611,2287,1070],{},[626,2289,1070],{"encoding":628},[579,2291,2293],{"className":2292,"ariaHidden":634},[633],[579,2294,2296,2299],{"className":2295},[638],[579,2297],{"className":2298,"style":956},[642],[579,2300,1070],{"className":2301},[647]," Stunden sind nicht ",[579,2304,2306,2336],{"className":2305},[586],[579,2307,2309],{"className":2308},[590],[592,2310,2311],{"xmlns":594},[597,2312,2313,2333],{},[600,2314,2315,2317,2319,2321,2323,2325,2327,2329,2331],{},[611,2316,1070],{},[607,2318,1119],{},[611,2320,787],{},[789,2322,791],{},[603,2324,795],{"mathvariant":794},[607,2326,609],{},[611,2328,885],{},[789,2330,791],{},[603,2332,795],{"mathvariant":794},[626,2334,2335],{"encoding":628},"3 \\cdot 25\\,\\% = 75\\,\\%",[579,2337,2339,2357,2381],{"className":2338,"ariaHidden":634},[633],[579,2340,2342,2345,2348,2351,2354],{"className":2341},[638],[579,2343],{"className":2344,"style":956},[642],[579,2346,1070],{"className":2347},[647],[579,2349],{"className":2350,"style":675},[653],[579,2352,1119],{"className":2353},[679],[579,2355],{"className":2356,"style":675},[653],[579,2358,2360,2363,2366,2369,2372,2375,2378],{"className":2359},[638],[579,2361],{"className":2362,"style":808},[642],[579,2364,787],{"className":2365},[647],[579,2367],{"className":2368,"style":815},[653],[579,2370,795],{"className":2371},[647],[579,2373],{"className":2374,"style":654},[653],[579,2376,609],{"className":2377},[658],[579,2379],{"className":2380,"style":654},[653],[579,2382,2384,2387,2390,2393],{"className":2383},[638],[579,2385],{"className":2386,"style":808},[642],[579,2388,885],{"className":2389},[647],[579,2391],{"className":2392,"style":815},[653],[579,2394,795],{"className":2395},[647]," weg (dann blieben ",[579,2398,2400,2427],{"className":2399},[586],[579,2401,2403],{"className":2402},[590],[592,2404,2405],{"xmlns":594},[597,2406,2407,2424],{},[600,2408,2409,2411,2413,2415,2417,2420,2422],{},[611,2410,1024],{},[607,2412,1119],{},[611,2414,2083],{},[607,2416,609],{},[611,2418,2419],{},"50",[789,2421,791],{},[789,2423,1029],{},[626,2425,2426],{"encoding":628},"200 \\cdot 0{,}25 = 50\\,\\text{mg}",[579,2428,2430,2448,2475],{"className":2429,"ariaHidden":634},[633],[579,2431,2433,2436,2439,2442,2445],{"className":2432},[638],[579,2434],{"className":2435,"style":956},[642],[579,2437,1024],{"className":2438},[647],[579,2440],{"className":2441,"style":675},[653],[579,2443,1119],{"className":2444},[679],[579,2446],{"className":2447,"style":675},[653],[579,2449,2451,2454,2457,2463,2466,2469,2472],{"className":2450},[638],[579,2452],{"className":2453,"style":869},[642],[579,2455,873],{"className":2456},[647],[579,2458,2460],{"className":2459},[647],[579,2461,881],{"className":2462},[880],[579,2464,787],{"className":2465},[647],[579,2467],{"className":2468,"style":654},[653],[579,2470,609],{"className":2471},[658],[579,2473],{"className":2474,"style":654},[653],[579,2476,2478,2481,2484,2487],{"className":2477},[638],[579,2479],{"className":2480,"style":869},[642],[579,2482,2419],{"className":2483},[647],[579,2485],{"className":2486,"style":815},[653],[579,2488,2490],{"className":2489},[647,1051],[579,2491,1029],{"className":2492},[647]," übrig), sondern knapp ",[579,2495,2497,2516],{"className":2496},[586],[579,2498,2500],{"className":2499},[590],[592,2501,2502],{"xmlns":594},[597,2503,2504,2513],{},[600,2505,2506,2509,2511],{},[611,2507,2508],{},"58",[789,2510,791],{},[603,2512,795],{"mathvariant":794},[626,2514,2515],{"encoding":628},"58\\,\\%",[579,2517,2519],{"className":2518,"ariaHidden":634},[633],[579,2520,2522,2525,2528,2531],{"className":2521},[638],[579,2523],{"className":2524,"style":808},[642],[579,2526,2508],{"className":2527},[647],[579,2529],{"className":2530,"style":815},[653],[579,2532,795],{"className":2533},[647],"; übrig sind ",[579,2536,2538,2556],{"className":2537},[586],[579,2539,2541],{"className":2540},[590],[592,2542,2543],{"xmlns":594},[597,2544,2545,2553],{},[600,2546,2547,2549,2551],{},[611,2548,1146],{},[789,2550,791],{},[789,2552,1029],{},[626,2554,2555],{"encoding":628},"84{,}4\\,\\text{mg}",[579,2557,2559],{"className":2558,"ariaHidden":634},[633],[579,2560,2562,2565,2568,2574,2577,2580],{"className":2561},[638],[579,2563],{"className":2564,"style":869},[642],[579,2566,1326],{"className":2567},[647],[579,2569,2571],{"className":2570},[647],[579,2572,881],{"className":2573},[880],[579,2575,1364],{"className":2576},[647],[579,2578],{"className":2579,"style":815},[653],[579,2581,2583],{"className":2582},[647,1051],[579,2584,1029],{"className":2585},[647],[2060,2587,2588,2589,2617,2618,2656,2657,2773],{},"Glauben, dass nach ",[579,2590,2592,2605],{"className":2591},[586],[579,2593,2595],{"className":2594},[590],[592,2596,2597],{"xmlns":594},[597,2598,2599,2603],{},[600,2600,2601],{},[611,2602,1364],{},[626,2604,1364],{"encoding":628},[579,2606,2608],{"className":2607,"ariaHidden":634},[633],[579,2609,2611,2614],{"className":2610},[638],[579,2612],{"className":2613,"style":956},[642],[579,2615,1364],{"className":2616},[647]," Schritten zu je ",[579,2619,2621,2638],{"className":2620},[586],[579,2622,2624],{"className":2623},[590],[592,2625,2626],{"xmlns":594},[597,2627,2628,2636],{},[600,2629,2630,2632,2634],{},[611,2631,787],{},[789,2633,791],{},[603,2635,795],{"mathvariant":794},[626,2637,798],{"encoding":628},[579,2639,2641],{"className":2640,"ariaHidden":634},[633],[579,2642,2644,2647,2650,2653],{"className":2643},[638],[579,2645],{"className":2646,"style":808},[642],[579,2648,787],{"className":2649},[647],[579,2651],{"className":2652,"style":815},[653],[579,2654,795],{"className":2655},[647]," alles weg ist: Es bleiben ",[579,2658,2660,2687],{"className":2659},[586],[579,2661,2663],{"className":2662},[590],[592,2664,2665],{"xmlns":594},[597,2666,2667,2684],{},[600,2668,2669,2675,2677,2680,2682],{},[1121,2670,2671,2673],{},[611,2672,838],{},[611,2674,1364],{},[607,2676,1143],{},[611,2678,2679],{},"31,6",[789,2681,791],{},[603,2683,795],{"mathvariant":794},[626,2685,2686],{"encoding":628},"0{,}75^4 \\approx 31{,}6\\,\\%",[579,2688,2690,2746],{"className":2689,"ariaHidden":634},[633],[579,2691,2693,2696,2699,2705,2708,2737,2740,2743],{"className":2692},[638],[579,2694],{"className":2695,"style":2121},[642],[579,2697,873],{"className":2698},[647],[579,2700,2702],{"className":2701},[647],[579,2703,881],{"className":2704},[880],[579,2706,1223],{"className":2707},[647],[579,2709,2711,2714],{"className":2710},[647],[579,2712,1230],{"className":2713},[647],[579,2715,2717],{"className":2716},[1234],[579,2718,2720],{"className":2719},[704],[579,2721,2723],{"className":2722},[709],[579,2724,2726],{"className":2725,"style":2152},[713],[579,2727,2728,2731],{"style":1797},[579,2729],{"className":2730,"style":1251},[721],[579,2732,2734],{"className":2733},[1255,1256,1257,1258],[579,2735,1364],{"className":2736},[647,1258],[579,2738],{"className":2739,"style":654},[653],[579,2741,1143],{"className":2742},[658],[579,2744],{"className":2745,"style":654},[653],[579,2747,2749,2753,2757,2763,2767,2770],{"className":2748},[638],[579,2750],{"className":2751,"style":2752},[642],"height:0.9444em;vertical-align:-0.1944em;",[579,2754,2756],{"className":2755},[647],"31",[579,2758,2760],{"className":2759},[647],[579,2761,881],{"className":2762},[880],[579,2764,2766],{"className":2765},[647],"6",[579,2768],{"className":2769,"style":815},[653],[579,2771,795],{"className":2772},[647]," übrig.",{"title":2775,"searchDepth":2776,"depth":2776,"links":2777},"",2,[2778,2779,2780],{"id":561,"depth":2776,"text":562},{"id":966,"depth":2776,"text":967},{"id":2054,"depth":2776,"text":2055},[2782,2785,2788,2794,2797,2803,2806,2809,2812,2815,2817,2819],{"lhs":2783,"rhs":2784},"N0*(1 - p\u002F100)^(t + 1)","N0*(1 - p\u002F100)^t * (1 - p\u002F100)",{"lhs":2786,"rhs":2787},"N0*(1 - p\u002F100)^t","N0*(1 + (-p)\u002F100)^t",{"lhs":2786,"rhs":2789,"where":2790},"84.375",{"N0":2791,"p":2792,"t":2793},200,25,3,{"lhs":2795,"rhs":2796},"0.75^3","0.421875",{"lhs":2798,"rhs":1529,"where":2799},"round(N0*(1 - p\u002F100)^t)",{"N0":2800,"p":2801,"t":2802},1500,8,5,{"lhs":2804,"rhs":2805},"round(0.92^5, 4)","0.6591",{"lhs":2807,"rhs":2808},"0.75^log(0.5, 0.75)","0.5",{"lhs":2810,"rhs":2811},"round(log(0.5, 0.75), 2)","2.41",{"lhs":2813,"rhs":2814},"200*0.25^3","3.125",{"lhs":2816,"rhs":2419},"200*(1 - 3*0.25)",{"lhs":2818,"rhs":2508},"round((1 - 0.75^3) * 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213.39 L 201.5 213.73 L 202.48 214.06 L 203.45 214.39 L 204.43 214.72 L 205.4 215.05 L 206.38 215.37 L 207.35 215.69 L 208.33 216 L 209.3 216.31 L 210.28 216.62 L 211.25 216.92 L 212.23 217.23 L 213.2 217.52 L 214.18 217.82 L 215.15 218.11 L 216.13 218.4 L 217.1 218.68 L 218.08 218.97 L 219.05 219.25 L 220.03 219.52 L 221 219.8 L 221.98 220.07 L 222.95 220.33 L 223.93 220.6 L 224.9 220.86 L 225.88 221.12 L 226.85 221.38 L 227.83 221.63 L 228.8 221.88 L 229.78 222.13 L 230.75 222.37 L 231.73 222.62 L 232.7 222.86 L 233.68 223.09 L 234.65 223.33 L 235.63 223.56 L 236.6 223.79 L 237.58 224.02 L 238.55 224.24 L 239.53 224.47 L 240.5 224.69 L 241.48 224.91 L 242.45 225.12 L 243.43 225.33 L 244.4 225.55 L 245.38 225.75 L 246.35 225.96 L 247.33 226.16 L 248.3 226.37 L 249.28 226.57 L 250.25 226.76 L 251.23 226.96 L 252.2 227.15 L 253.18 227.35 L 254.15 227.53 L 255.13 227.72 L 256.1 227.91 L 257.08 228.09 L 258.05 228.27 L 259.03 228.45 L 260 228.63 L 260.98 228.81 L 261.95 228.98 L 262.93 229.15 L 263.9 229.32 L 264.88 229.49 L 265.85 229.66 L 266.83 229.82 L 267.8 229.98\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-exponential-decay-clip)\"\u002F>\u003Ccircle cx=\"33.8\" cy=\"45\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"41.8\" y=\"37\" 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=\"111.8\" cy=\"160.63\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"119.8\" y=\"150.63\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">(3 | 84,4)\u003C\u002Ftext>\u003Ctext x=\"202.8\" y=\"200\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">N\u003C\u002Ftext>\u003C\u002Fsvg>","exponential-decay","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 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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\u002Fexponentielle-abnahme",[],[2877,2878,2879],"exponential-growth","half-life","exponential-function",{"title":548,"description":2775},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielle-abnahme","Nimmt ein Bestand pro Zeitschritt um p % ab, bleibt nach t Schritten N₀ · (1 − p\u002F100)ᵗ übrig.",[2884,2885,2886,2887],"exponentielle abnahme","zerfall","abnahmefaktor","prozent",[2889,2893,2896,2899,2902],{"symbol":2890,"meaning":2891,"symbolHtml":2892},"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":2855,"meaning":2894,"symbolHtml":2895},"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 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style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1711,"meaning":2900,"symbolHtml":2901},"Anzahl der Zeitschritte","\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>",{"symbol":2903,"meaning":2904,"symbolHtml":2905},"1 - \\frac{p}{100}","Abnahmefaktor, liegt zwischen 0 und 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>100\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1 - \\frac{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:0.7278em;vertical-align:-0.0833em;\">\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0925em;vertical-align:-0.345em;\">\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:0.7475em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">100\u003C\u002Fspan>\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:-3.4461em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\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:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","ybZdDsxjS3OFiaZ09k_gSTPDSAxzAqyuSdl6_uHROio",[2908,2911,2914],{"stem":2909,"title":2910,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentialfunktion","Exponentialfunktion",{"stem":2912,"title":2913,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum","Exponentielles Wachstum",{"stem":2915,"title":2916,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fhalbwertszeit","Halbwertszeit",1793824274218]