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Das Sättigungsmanko selbst nimmt exponentiell ab: ",[578,950,952,1011],{"className":951},[581],[578,953,955],{"className":954},[585],[587,956,957],{"xmlns":589},[591,958,959,1008],{},[594,960,961,963,965,967,969,971,973,975,977,979,981,983,985,989,991,993,995],{},[597,962,599],{},[640,964,642],{},[597,966,645],{},[640,968,649],{"stretchy":648},[597,970,652],{},[640,972,655],{"stretchy":648},[640,974,745],{},[640,976,649],{"fence":608,"stretchy":608,"minsize":754,"maxsize":754},[597,978,599],{},[640,980,642],{},[597,982,645],{},[640,984,649],{"stretchy":648},[986,987,988],"mn",{},"0",[640,990,655],{"stretchy":648},[640,992,655],{"fence":608,"stretchy":608,"minsize":754,"maxsize":754},[640,994,751],{},[728,996,997,1000],{},[597,998,999],{},"e",[594,1001,1002,1004,1006],{},[640,1003,642],{},[597,1005,748],{},[597,1007,652],{},[601,1009,1010],{"encoding":603},"S - f(t) = \\bigl(S - f(0)\\bigr) \\cdot e^{-kt}",[578,1012,1014,1032,1059,1083,1116],{"className":1013,"ariaHidden":608},[607],[578,1015,1017,1020,1023,1026,1029],{"className":1016},[612],[578,1018],{"className":1019,"style":668},[616],[578,1021,599],{"className":1022,"style":623},[621,622],[578,1024],{"className":1025,"style":676},[675],[578,1027,642],{"className":1028},[680],[578,1030],{"className":1031,"style":676},[675],[578,1033,1035,1038,1041,1044,1047,1050,1053,1056],{"className":1034},[612],[578,1036],{"className":1037,"style":690},[616],[578,1039,645],{"className":1040,"style":694},[621,622],[578,1042,649],{"className":1043},[698],[578,1045,652],{"className":1046},[621,622],[578,1048,655],{"className":1049},[705],[578,1051],{"className":1052,"style":838},[675],[578,1054,745],{"className":1055},[842],[578,1057],{"className":1058,"style":838},[675],[578,1060,1062,1065,1071,1074,1077,1080],{"className":1061},[612],[578,1063],{"className":1064,"style":872},[616],[578,1066,1068],{"className":1067},[698],[578,1069,649],{"className":1070},[879,880],[578,1072,599],{"className":1073,"style":623},[621,622],[578,1075],{"className":1076,"style":676},[675],[578,1078,642],{"className":1079},[680],[578,1081],{"className":1082,"style":676},[675],[578,1084,1086,1089,1092,1095,1098,1101,1107,1110,1113],{"className":1085},[612],[578,1087],{"className":1088,"style":872},[616],[578,1090,645],{"className":1091,"style":694},[621,622],[578,1093,649],{"className":1094},[698],[578,1096,988],{"className":1097},[621],[578,1099,655],{"className":1100},[705],[578,1102,1104],{"className":1103},[705],[578,1105,655],{"className":1106},[879,880],[578,1108],{"className":1109,"style":676},[675],[578,1111,751],{"className":1112},[680],[578,1114],{"className":1115,"style":676},[675],[578,1117,1119,1123],{"className":1118},[612],[578,1120],{"className":1121,"style":1122},[616],"height:0.8491em;",[578,1124,1126,1129],{"className":1125},[621],[578,1127,999],{"className":1128},[621,622],[578,1130,1132],{"className":1131},[791],[578,1133,1135],{"className":1134},[795],[578,1136,1138],{"className":1137},[799],[578,1139,1141],{"className":1140,"style":1122},[803],[578,1142,1144,1147],{"style":1143},"top:-3.063em;margin-right:0.05em;",[578,1145],{"className":1146,"style":812},[811],[578,1148,1150],{"className":1149},[816,817,818,819],[578,1151,1153,1156,1159],{"className":1152},[621,819],[578,1154,642],{"className":1155},[621,819],[578,1157,748],{"className":1158,"style":856},[621,622,819],[578,1160,652],{"className":1161},[621,622,819],". Daraus folgt die Formel.",[565,1164,1165,1166,1194,1195,1223,1224,1226],{},"Typische Anwendungen sind Abkühlen und Erwärmen (die Schranke ist die Umgebungstemperatur), Lernkurven oder die Verbreitung eines Produkts mit fester Zielgruppe. Liegt der Anfangswert über ",[578,1167,1169,1182],{"className":1168},[581],[578,1170,1172],{"className":1171},[585],[587,1173,1174],{"xmlns":589},[591,1175,1176,1180],{},[594,1177,1178],{},[597,1179,599],{},[601,1181,599],{"encoding":603},[578,1183,1185],{"className":1184,"ariaHidden":608},[607],[578,1186,1188,1191],{"className":1187},[612],[578,1189],{"className":1190,"style":617},[616],[578,1192,599],{"className":1193,"style":623},[621,622],", fällt der Bestand von oben auf ",[578,1196,1198,1211],{"className":1197},[581],[578,1199,1201],{"className":1200},[585],[587,1202,1203],{"xmlns":589},[591,1204,1205,1209],{},[594,1206,1207],{},[597,1208,599],{},[601,1210,599],{"encoding":603},[578,1212,1214],{"className":1213,"ariaHidden":608},[607],[578,1215,1217,1220],{"className":1216},[612],[578,1218],{"className":1219,"style":617},[616],[578,1221,599],{"className":1222,"style":623},[621,622]," zu; die Formel gilt dann unverändert (",[569,1225,555],{},").",[565,1228,1229,1230,1284,1285,1359,1360,1388,1389,1433,1434,1462],{},"Die Bedingung ",[578,1231,1233,1252],{"className":1232},[581],[578,1234,1236],{"className":1235},[585],[587,1237,1238],{"xmlns":589},[591,1239,1240,1249],{},[594,1241,1242,1244,1247],{},[597,1243,748],{},[640,1245,1246],{},">",[986,1248,988],{},[601,1250,1251],{"encoding":603},"k > 0",[578,1253,1255,1274],{"className":1254,"ariaHidden":608},[607],[578,1256,1258,1262,1265,1268,1271],{"className":1257},[612],[578,1259],{"className":1260,"style":1261},[616],"height:0.7335em;vertical-align:-0.0391em;",[578,1263,748],{"className":1264,"style":856},[621,622],[578,1266],{"className":1267,"style":838},[675],[578,1269,1246],{"className":1270},[842],[578,1272],{"className":1273,"style":838},[675],[578,1275,1277,1281],{"className":1276},[612],[578,1278],{"className":1279,"style":1280},[616],"height:0.6444em;",[578,1282,988],{"className":1283},[621]," sorgt dafür, dass ",[578,1286,1288,1312],{"className":1287},[581],[578,1289,1291],{"className":1290},[585],[587,1292,1293],{"xmlns":589},[591,1294,1295,1309],{},[594,1296,1297],{},[728,1298,1299,1301],{},[597,1300,999],{},[594,1302,1303,1305,1307],{},[640,1304,642],{},[597,1306,748],{},[597,1308,652],{},[601,1310,1311],{"encoding":603},"e^{-kt}",[578,1313,1315],{"className":1314,"ariaHidden":608},[607],[578,1316,1318,1321],{"className":1317},[612],[578,1319],{"className":1320,"style":1122},[616],[578,1322,1324,1327],{"className":1323},[621],[578,1325,999],{"className":1326},[621,622],[578,1328,1330],{"className":1329},[791],[578,1331,1333],{"className":1332},[795],[578,1334,1336],{"className":1335},[799],[578,1337,1339],{"className":1338,"style":1122},[803],[578,1340,1341,1344],{"style":1143},[578,1342],{"className":1343,"style":812},[811],[578,1345,1347],{"className":1346},[816,817,818,819],[578,1348,1350,1353,1356],{"className":1349},[621,819],[578,1351,642],{"className":1352},[621,819],[578,1354,748],{"className":1355,"style":856},[621,622,819],[578,1357,652],{"className":1358},[621,622,819]," gegen ",[578,1361,1363,1376],{"className":1362},[581],[578,1364,1366],{"className":1365},[585],[587,1367,1368],{"xmlns":589},[591,1369,1370,1374],{},[594,1371,1372],{},[986,1373,988],{},[601,1375,988],{"encoding":603},[578,1377,1379],{"className":1378,"ariaHidden":608},[607],[578,1380,1382,1385],{"className":1381},[612],[578,1383],{"className":1384,"style":1280},[616],[578,1386,988],{"className":1387},[621]," geht und ",[578,1390,1392,1412],{"className":1391},[581],[578,1393,1395],{"className":1394},[585],[587,1396,1397],{"xmlns":589},[591,1398,1399,1409],{},[594,1400,1401,1403,1405,1407],{},[597,1402,645],{},[640,1404,649],{"stretchy":648},[597,1406,652],{},[640,1408,655],{"stretchy":648},[601,1410,1411],{"encoding":603},"f(t)",[578,1413,1415],{"className":1414,"ariaHidden":608},[607],[578,1416,1418,1421,1424,1427,1430],{"className":1417},[612],[578,1419],{"className":1420,"style":690},[616],[578,1422,645],{"className":1423,"style":694},[621,622],[578,1425,649],{"className":1426},[698],[578,1428,652],{"className":1429},[621,622],[578,1431,655],{"className":1432},[705]," sich tatsächlich ",[578,1435,1437,1450],{"className":1436},[581],[578,1438,1440],{"className":1439},[585],[587,1441,1442],{"xmlns":589},[591,1443,1444,1448],{},[594,1445,1446],{},[597,1447,599],{},[601,1449,599],{"encoding":603},[578,1451,1453],{"className":1452,"ariaHidden":608},[607],[578,1454,1456,1459],{"className":1455},[612],[578,1457],{"className":1458,"style":617},[616],[578,1460,599],{"className":1461,"style":623},[621,622]," nähert.",[560,1464,1466],{"id":1465},"beispiele","Beispiele",[565,1468,1469,1470,1554,1555,1632,1633,1698,1699,1728],{},"Ein Tee hat ",[578,1471,1473,1502],{"className":1472},[581],[578,1474,1476],{"className":1475},[585],[587,1477,1478],{"xmlns":589},[591,1479,1480,1499],{},[594,1481,1482,1485,1489,1496],{},[986,1483,1484],{},"90",[1486,1487,1488],"mtext",{}," ",[728,1490,1491,1493],{},[594,1492],{},[640,1494,1495],{},"∘",[1486,1497,1498],{},"C",[601,1500,1501],{"encoding":603},"90\\,^\\circ\\text{C}",[578,1503,1505],{"className":1504,"ariaHidden":608},[607],[578,1506,1508,1511,1514,1518,1547],{"className":1507},[612],[578,1509],{"className":1510,"style":617},[616],[578,1512,1484],{"className":1513},[621],[578,1515],{"className":1516,"style":1517},[675],"margin-right:0.1667em;",[578,1519,1521,1523],{"className":1520},[621],[578,1522],{},[578,1524,1526],{"className":1525},[791],[578,1527,1529],{"className":1528},[795],[578,1530,1532],{"className":1531},[799],[578,1533,1536],{"className":1534,"style":1535},[803],"height:0.6741em;",[578,1537,1538,1541],{"style":1143},[578,1539],{"className":1540,"style":812},[811],[578,1542,1544],{"className":1543},[816,817,818,819],[578,1545,1495],{"className":1546},[680,819],[578,1548,1551],{"className":1549},[621,1550],"text",[578,1552,1498],{"className":1553},[621]," und kühlt in einem ",[578,1556,1558,1583],{"className":1557},[581],[578,1559,1561],{"className":1560},[585],[587,1562,1563],{"xmlns":589},[591,1564,1565,1580],{},[594,1566,1567,1570,1572,1578],{},[986,1568,1569],{},"20",[1486,1571,1488],{},[728,1573,1574,1576],{},[594,1575],{},[640,1577,1495],{},[1486,1579,1498],{},[601,1581,1582],{"encoding":603},"20\\,^\\circ\\text{C}",[578,1584,1586],{"className":1585,"ariaHidden":608},[607],[578,1587,1589,1592,1595,1598,1626],{"className":1588},[612],[578,1590],{"className":1591,"style":617},[616],[578,1593,1569],{"className":1594},[621],[578,1596],{"className":1597,"style":1517},[675],[578,1599,1601,1603],{"className":1600},[621],[578,1602],{},[578,1604,1606],{"className":1605},[791],[578,1607,1609],{"className":1608},[795],[578,1610,1612],{"className":1611},[799],[578,1613,1615],{"className":1614,"style":1535},[803],[578,1616,1617,1620],{"style":1143},[578,1618],{"className":1619,"style":812},[811],[578,1621,1623],{"className":1622},[816,817,818,819],[578,1624,1495],{"className":1625},[680,819],[578,1627,1629],{"className":1628},[621,1550],[578,1630,1498],{"className":1631},[621]," warmen Raum ab, mit ",[578,1634,1636,1655],{"className":1635},[581],[578,1637,1639],{"className":1638},[585],[587,1640,1641],{"xmlns":589},[591,1642,1643,1652],{},[594,1644,1645,1647,1649],{},[597,1646,748],{},[640,1648,745],{},[986,1650,1651],{},"0,05",[601,1653,1654],{"encoding":603},"k = 0{,}05",[578,1656,1658,1676],{"className":1657,"ariaHidden":608},[607],[578,1659,1661,1664,1667,1670,1673],{"className":1660},[612],[578,1662],{"className":1663,"style":852},[616],[578,1665,748],{"className":1666,"style":856},[621,622],[578,1668],{"className":1669,"style":838},[675],[578,1671,745],{"className":1672},[842],[578,1674],{"className":1675,"style":838},[675],[578,1677,1679,1683,1686,1694],{"className":1678},[612],[578,1680],{"className":1681,"style":1682},[616],"height:0.8389em;vertical-align:-0.1944em;",[578,1684,988],{"className":1685},[621],[578,1687,1689],{"className":1688},[621],[578,1690,1693],{"className":1691},[1692],"mpunct",",",[578,1695,1697],{"className":1696},[621],"05"," pro Minute. Nach ",[578,1700,1702,1716],{"className":1701},[581],[578,1703,1705],{"className":1704},[585],[587,1706,1707],{"xmlns":589},[591,1708,1709,1714],{},[594,1710,1711],{},[986,1712,1713],{},"10",[601,1715,1713],{"encoding":603},[578,1717,1719],{"className":1718,"ariaHidden":608},[607],[578,1720,1722,1725],{"className":1721},[612],[578,1723],{"className":1724,"style":1280},[616],[578,1726,1713],{"className":1727},[621]," Minuten:",[578,1730,1732],{"className":1731},[713],[578,1733,1735,1826],{"className":1734},[581],[578,1736,1738],{"className":1737},[585],[587,1739,1740],{"xmlns":589,"display":722},[591,1741,1742,1823],{},[594,1743,1744,1746,1748,1750,1752,1754,1756,1758,1760,1762,1764,1766,1768,1770,1784,1786,1788,1791,1794,1796,1807,1810,1813,1815,1821],{},[597,1745,645],{},[640,1747,649],{"stretchy":648},[986,1749,1713],{},[640,1751,655],{"stretchy":648},[640,1753,745],{},[986,1755,1569],{},[640,1757,642],{},[640,1759,649],{"stretchy":648},[986,1761,1569],{},[640,1763,642],{},[986,1765,1484],{},[640,1767,655],{"stretchy":648},[640,1769,751],{},[728,1771,1772,1774],{},[597,1773,999],{},[594,1775,1776,1778,1780,1782],{},[640,1777,642],{},[986,1779,1651],{},[640,1781,751],{},[986,1783,1713],{},[640,1785,745],{},[986,1787,1569],{},[640,1789,1790],{},"+",[986,1792,1793],{},"70",[640,1795,751],{},[728,1797,1798,1800],{},[597,1799,999],{},[594,1801,1802,1804],{},[640,1803,642],{},[986,1805,1806],{},"0,5",[640,1808,1809],{},"≈",[986,1811,1812],{},"62,5",[1486,1814,1488],{},[728,1816,1817,1819],{},[594,1818],{},[640,1820,1495],{},[1486,1822,1498],{},[601,1824,1825],{"encoding":603},"f(10) = 20 - (20 - 90) \\cdot e^{-0{,}05 \\cdot 10} = 20 + 70 \\cdot e^{-0{,}5} \\approx 62{,}5\\,^\\circ\\text{C}",[578,1827,1829,1856,1875,1896,1917,1983,2001,2019,2079],{"className":1828,"ariaHidden":608},[607],[578,1830,1832,1835,1838,1841,1844,1847,1850,1853],{"className":1831},[612],[578,1833],{"className":1834,"style":690},[616],[578,1836,645],{"className":1837,"style":694},[621,622],[578,1839,649],{"className":1840},[698],[578,1842,1713],{"className":1843},[621],[578,1845,655],{"className":1846},[705],[578,1848],{"className":1849,"style":838},[675],[578,1851,745],{"className":1852},[842],[578,1854],{"className":1855,"style":838},[675],[578,1857,1859,1863,1866,1869,1872],{"className":1858},[612],[578,1860],{"className":1861,"style":1862},[616],"height:0.7278em;vertical-align:-0.0833em;",[578,1864,1569],{"className":1865},[621],[578,1867],{"className":1868,"style":676},[675],[578,1870,642],{"className":1871},[680],[578,1873],{"className":1874,"style":676},[675],[578,1876,1878,1881,1884,1887,1890,1893],{"className":1877},[612],[578,1879],{"className":1880,"style":690},[616],[578,1882,649],{"className":1883},[698],[578,1885,1569],{"className":1886},[621],[578,1888],{"className":1889,"style":676},[675],[578,1891,642],{"className":1892},[680],[578,1894],{"className":1895,"style":676},[675],[578,1897,1899,1902,1905,1908,1911,1914],{"className":1898},[612],[578,1900],{"className":1901,"style":690},[616],[578,1903,1484],{"className":1904},[621],[578,1906,655],{"className":1907},[705],[578,1909],{"className":1910,"style":676},[675],[578,1912,751],{"className":1913},[680],[578,1915],{"className":1916,"style":676},[675],[578,1918,1920,1924,1974,1977,1980],{"className":1919},[612],[578,1921],{"className":1922,"style":1923},[616],"height:0.8641em;",[578,1925,1927,1930],{"className":1926},[621],[578,1928,999],{"className":1929},[621,622],[578,1931,1933],{"className":1932},[791],[578,1934,1936],{"className":1935},[795],[578,1937,1939],{"className":1938},[799],[578,1940,1942],{"className":1941,"style":1923},[803],[578,1943,1944,1947],{"style":807},[578,1945],{"className":1946,"style":812},[811],[578,1948,1950],{"className":1949},[816,817,818,819],[578,1951,1953,1956,1959,1965,1968,1971],{"className":1952},[621,819],[578,1954,642],{"className":1955},[621,819],[578,1957,988],{"className":1958},[621,819],[578,1960,1962],{"className":1961},[621,819],[578,1963,1693],{"className":1964},[1692,819],[578,1966,1697],{"className":1967},[621,819],[578,1969,751],{"className":1970},[680,819],[578,1972,1713],{"className":1973},[621,819],[578,1975],{"className":1976,"style":838},[675],[578,1978,745],{"className":1979},[842],[578,1981],{"className":1982,"style":838},[675],[578,1984,1986,1989,1992,1995,1998],{"className":1985},[612],[578,1987],{"className":1988,"style":1862},[616],[578,1990,1569],{"className":1991},[621],[578,1993],{"className":1994,"style":676},[675],[578,1996,1790],{"className":1997},[680],[578,1999],{"className":2000,"style":676},[675],[578,2002,2004,2007,2010,2013,2016],{"className":2003},[612],[578,2005],{"className":2006,"style":1280},[616],[578,2008,1793],{"className":2009},[621],[578,2011],{"className":2012,"style":676},[675],[578,2014,751],{"className":2015},[680],[578,2017],{"className":2018,"style":676},[675],[578,2020,2022,2025,2070,2073,2076],{"className":2021},[612],[578,2023],{"className":2024,"style":1923},[616],[578,2026,2028,2031],{"className":2027},[621],[578,2029,999],{"className":2030},[621,622],[578,2032,2034],{"className":2033},[791],[578,2035,2037],{"className":2036},[795],[578,2038,2040],{"className":2039},[799],[578,2041,2043],{"className":2042,"style":1923},[803],[578,2044,2045,2048],{"style":807},[578,2046],{"className":2047,"style":812},[811],[578,2049,2051],{"className":2050},[816,817,818,819],[578,2052,2054,2057,2060,2066],{"className":2053},[621,819],[578,2055,642],{"className":2056},[621,819],[578,2058,988],{"className":2059},[621,819],[578,2061,2063],{"className":2062},[621,819],[578,2064,1693],{"className":2065},[1692,819],[578,2067,2069],{"className":2068},[621,819],"5",[578,2071],{"className":2072,"style":838},[675],[578,2074,1809],{"className":2075},[842],[578,2077],{"className":2078,"style":838},[675],[578,2080,2082,2086,2090,2096,2099,2102,2131],{"className":2081},[612],[578,2083],{"className":2084,"style":2085},[616],"height:0.9186em;vertical-align:-0.1944em;",[578,2087,2089],{"className":2088},[621],"62",[578,2091,2093],{"className":2092},[621],[578,2094,1693],{"className":2095},[1692],[578,2097,2069],{"className":2098},[621],[578,2100],{"className":2101,"style":1517},[675],[578,2103,2105,2107],{"className":2104},[621],[578,2106],{},[578,2108,2110],{"className":2109},[791],[578,2111,2113],{"className":2112},[795],[578,2114,2116],{"className":2115},[799],[578,2117,2120],{"className":2118,"style":2119},[803],"height:0.7241em;",[578,2121,2122,2125],{"style":807},[578,2123],{"className":2124,"style":812},[811],[578,2126,2128],{"className":2127},[816,817,818,819],[578,2129,1495],{"className":2130},[680,819],[578,2132,2134],{"className":2133},[621,1550],[578,2135,1498],{"className":2136},[621],[565,2138,2139,2140,2217,2218,2368,2369,2558],{},"Wann hat der Tee ",[578,2141,2143,2168],{"className":2142},[581],[578,2144,2146],{"className":2145},[585],[587,2147,2148],{"xmlns":589},[591,2149,2150,2165],{},[594,2151,2152,2155,2157,2163],{},[986,2153,2154],{},"50",[1486,2156,1488],{},[728,2158,2159,2161],{},[594,2160],{},[640,2162,1495],{},[1486,2164,1498],{},[601,2166,2167],{"encoding":603},"50\\,^\\circ\\text{C}",[578,2169,2171],{"className":2170,"ariaHidden":608},[607],[578,2172,2174,2177,2180,2183,2211],{"className":2173},[612],[578,2175],{"className":2176,"style":617},[616],[578,2178,2154],{"className":2179},[621],[578,2181],{"className":2182,"style":1517},[675],[578,2184,2186,2188],{"className":2185},[621],[578,2187],{},[578,2189,2191],{"className":2190},[791],[578,2192,2194],{"className":2193},[795],[578,2195,2197],{"className":2196},[799],[578,2198,2200],{"className":2199,"style":1535},[803],[578,2201,2202,2205],{"style":1143},[578,2203],{"className":2204,"style":812},[811],[578,2206,2208],{"className":2207},[816,817,818,819],[578,2209,1495],{"className":2210},[680,819],[578,2212,2214],{"className":2213},[621,1550],[578,2215,1498],{"className":2216},[621],"? Aus ",[578,2219,2221,2257],{"className":2220},[581],[578,2222,2224],{"className":2223},[585],[587,2225,2226],{"xmlns":589},[591,2227,2228,2254],{},[594,2229,2230,2232,2234,2236,2238,2250,2252],{},[986,2231,1569],{},[640,2233,1790],{},[986,2235,1793],{},[640,2237,751],{},[728,2239,2240,2242],{},[597,2241,999],{},[594,2243,2244,2246,2248],{},[640,2245,642],{},[986,2247,1651],{},[597,2249,652],{},[640,2251,745],{},[986,2253,2154],{},[601,2255,2256],{"encoding":603},"20 + 70 \\cdot e^{-0{,}05t} = 50",[578,2258,2260,2278,2296,2359],{"className":2259,"ariaHidden":608},[607],[578,2261,2263,2266,2269,2272,2275],{"className":2262},[612],[578,2264],{"className":2265,"style":1862},[616],[578,2267,1569],{"className":2268},[621],[578,2270],{"className":2271,"style":676},[675],[578,2273,1790],{"className":2274},[680],[578,2276],{"className":2277,"style":676},[675],[578,2279,2281,2284,2287,2290,2293],{"className":2280},[612],[578,2282],{"className":2283,"style":1280},[616],[578,2285,1793],{"className":2286},[621],[578,2288],{"className":2289,"style":676},[675],[578,2291,751],{"className":2292},[680],[578,2294],{"className":2295,"style":676},[675],[578,2297,2299,2303,2350,2353,2356],{"className":2298},[612],[578,2300],{"className":2301,"style":2302},[616],"height:0.8141em;",[578,2304,2306,2309],{"className":2305},[621],[578,2307,999],{"className":2308},[621,622],[578,2310,2312],{"className":2311},[791],[578,2313,2315],{"className":2314},[795],[578,2316,2318],{"className":2317},[799],[578,2319,2321],{"className":2320,"style":2302},[803],[578,2322,2323,2326],{"style":1143},[578,2324],{"className":2325,"style":812},[811],[578,2327,2329],{"className":2328},[816,817,818,819],[578,2330,2332,2335,2338,2344,2347],{"className":2331},[621,819],[578,2333,642],{"className":2334},[621,819],[578,2336,988],{"className":2337},[621,819],[578,2339,2341],{"className":2340},[621,819],[578,2342,1693],{"className":2343},[1692,819],[578,2345,1697],{"className":2346},[621,819],[578,2348,652],{"className":2349},[621,622,819],[578,2351],{"className":2352,"style":838},[675],[578,2354,745],{"className":2355},[842],[578,2357],{"className":2358,"style":838},[675],[578,2360,2362,2365],{"className":2361},[612],[578,2363],{"className":2364,"style":1280},[616],[578,2366,2154],{"className":2367},[621]," folgt ",[578,2370,2372,2406],{"className":2371},[581],[578,2373,2375],{"className":2374},[585],[587,2376,2377],{"xmlns":589},[591,2378,2379,2403],{},[594,2380,2381,2393,2395],{},[728,2382,2383,2385],{},[597,2384,999],{},[594,2386,2387,2389,2391],{},[640,2388,642],{},[986,2390,1651],{},[597,2392,652],{},[640,2394,745],{},[2396,2397,2398,2401],"mfrac",{},[986,2399,2400],{},"30",[986,2402,1793],{},[601,2404,2405],{"encoding":603},"e^{-0{,}05t} = \\frac{30}{70}",[578,2407,2409,2471],{"className":2408,"ariaHidden":608},[607],[578,2410,2412,2415,2462,2465,2468],{"className":2411},[612],[578,2413],{"className":2414,"style":2302},[616],[578,2416,2418,2421],{"className":2417},[621],[578,2419,999],{"className":2420},[621,622],[578,2422,2424],{"className":2423},[791],[578,2425,2427],{"className":2426},[795],[578,2428,2430],{"className":2429},[799],[578,2431,2433],{"className":2432,"style":2302},[803],[578,2434,2435,2438],{"style":1143},[578,2436],{"className":2437,"style":812},[811],[578,2439,2441],{"className":2440},[816,817,818,819],[578,2442,2444,2447,2450,2456,2459],{"className":2443},[621,819],[578,2445,642],{"className":2446},[621,819],[578,2448,988],{"className":2449},[621,819],[578,2451,2453],{"className":2452},[621,819],[578,2454,1693],{"className":2455},[1692,819],[578,2457,1697],{"className":2458},[621,819],[578,2460,652],{"className":2461},[621,622,819],[578,2463],{"className":2464,"style":838},[675],[578,2466,745],{"className":2467},[842],[578,2469],{"className":2470,"style":838},[675],[578,2472,2474,2478],{"className":2473},[612],[578,2475],{"className":2476,"style":2477},[616],"height:1.1901em;vertical-align:-0.345em;",[578,2479,2481,2485,2555],{"className":2480},[621],[578,2482],{"className":2483},[698,2484],"nulldelimiter",[578,2486,2488],{"className":2487},[2396],[578,2489,2492,2546],{"className":2490},[795,2491],"vlist-t2",[578,2493,2495,2541],{"className":2494},[799],[578,2496,2499,2515,2526],{"className":2497,"style":2498},[803],"height:0.8451em;",[578,2500,2502,2506],{"style":2501},"top:-2.655em;",[578,2503],{"className":2504,"style":2505},[811],"height:3em;",[578,2507,2509],{"className":2508},[816,817,818,819],[578,2510,2512],{"className":2511},[621,819],[578,2513,1793],{"className":2514},[621,819],[578,2516,2518,2521],{"style":2517},"top:-3.23em;",[578,2519],{"className":2520,"style":2505},[811],[578,2522],{"className":2523,"style":2525},[2524],"frac-line","border-bottom-width:0.04em;",[578,2527,2529,2532],{"style":2528},"top:-3.394em;",[578,2530],{"className":2531,"style":2505},[811],[578,2533,2535],{"className":2534},[816,817,818,819],[578,2536,2538],{"className":2537},[621,819],[578,2539,2400],{"className":2540},[621,819],[578,2542,2545],{"className":2543},[2544],"vlist-s","​",[578,2547,2549],{"className":2548},[799],[578,2550,2553],{"className":2551,"style":2552},[803],"height:0.345em;",[578,2554],{},[578,2556],{"className":2557},[705,2484],", also",[578,2560,2562],{"className":2561},[713],[578,2563,2565,2613],{"className":2564},[581],[578,2566,2568],{"className":2567},[585],[587,2569,2570],{"xmlns":589,"display":722},[591,2571,2572,2610],{},[594,2573,2574,2576,2578,2602,2604,2607],{},[597,2575,652],{},[640,2577,745],{},[2396,2579,2580,2600],{},[594,2581,2582,2585,2588],{},[597,2583,2584],{},"ln",[640,2586,2587],{},"⁡",[594,2589,2590,2592,2598],{},[640,2591,649],{"fence":608},[2396,2593,2594,2596],{},[986,2595,1793],{},[986,2597,2400],{},[640,2599,655],{"fence":608},[986,2601,1651],{},[640,2603,1809],{},[986,2605,2606],{},"16,9",[1486,2608,2609],{}," Minuten",[601,2611,2612],{"encoding":603},"t = \\frac{\\ln\\left(\\frac{70}{30}\\right)}{0{,}05} \\approx 16{,}9 \\text{ Minuten}",[578,2614,2616,2635,2816],{"className":2615,"ariaHidden":608},[607],[578,2617,2619,2623,2626,2629,2632],{"className":2618},[612],[578,2620],{"className":2621,"style":2622},[616],"height:0.6151em;",[578,2624,652],{"className":2625},[621,622],[578,2627],{"className":2628,"style":838},[675],[578,2630,745],{"className":2631},[842],[578,2633],{"className":2634,"style":838},[675],[578,2636,2638,2642,2807,2810,2813],{"className":2637},[612],[578,2639],{"className":2640,"style":2641},[616],"height:2.4705em;vertical-align:-0.8804em;",[578,2643,2645,2648,2804],{"className":2644},[621],[578,2646],{"className":2647},[698,2484],[578,2649,2651],{"className":2650},[2396],[578,2652,2654,2795],{"className":2653},[795,2491],[578,2655,2657,2792],{"className":2656},[799],[578,2658,2661,2682,2690],{"className":2659,"style":2660},[803],"height:1.59em;",[578,2662,2664,2667],{"style":2663},"top:-2.314em;",[578,2665],{"className":2666,"style":2505},[811],[578,2668,2670,2673,2679],{"className":2669},[621],[578,2671,988],{"className":2672},[621],[578,2674,2676],{"className":2675},[621],[578,2677,1693],{"className":2678},[1692],[578,2680,1697],{"className":2681},[621],[578,2683,2684,2687],{"style":2517},[578,2685],{"className":2686,"style":2505},[811],[578,2688],{"className":2689,"style":2525},[2524],[578,2691,2693,2696],{"style":2692},"top:-3.74em;",[578,2694],{"className":2695,"style":2505},[811],[578,2697,2699,2703,2706],{"className":2698},[621],[578,2700,2584],{"className":2701},[2702],"mop",[578,2704],{"className":2705,"style":1517},[675],[578,2707,2710,2718,2786],{"className":2708},[2709],"minner",[578,2711,2715],{"className":2712,"style":2714},[698,2713],"delimcenter","top:0em;",[578,2716,649],{"className":2717},[879,880],[578,2719,2721,2724,2783],{"className":2720},[621],[578,2722],{"className":2723},[698,2484],[578,2725,2727],{"className":2726},[2396],[578,2728,2730,2775],{"className":2729},[795,2491],[578,2731,2733,2772],{"className":2732},[799],[578,2734,2736,2750,2758],{"className":2735,"style":2498},[803],[578,2737,2738,2741],{"style":2501},[578,2739],{"className":2740,"style":2505},[811],[578,2742,2744],{"className":2743},[816,817,818,819],[578,2745,2747],{"className":2746},[621,819],[578,2748,2400],{"className":2749},[621,819],[578,2751,2752,2755],{"style":2517},[578,2753],{"className":2754,"style":2505},[811],[578,2756],{"className":2757,"style":2525},[2524],[578,2759,2760,2763],{"style":2528},[578,2761],{"className":2762,"style":2505},[811],[578,2764,2766],{"className":2765},[816,817,818,819],[578,2767,2769],{"className":2768},[621,819],[578,2770,1793],{"className":2771},[621,819],[578,2773,2545],{"className":2774},[2544],[578,2776,2778],{"className":2777},[799],[578,2779,2781],{"className":2780,"style":2552},[803],[578,2782],{},[578,2784],{"className":2785},[705,2484],[578,2787,2789],{"className":2788,"style":2714},[705,2713],[578,2790,655],{"className":2791},[879,880],[578,2793,2545],{"className":2794},[2544],[578,2796,2798],{"className":2797},[799],[578,2799,2802],{"className":2800,"style":2801},[803],"height:0.8804em;",[578,2803],{},[578,2805],{"className":2806},[705,2484],[578,2808],{"className":2809,"style":838},[675],[578,2811,1809],{"className":2812},[842],[578,2814],{"className":2815,"style":838},[675],[578,2817,2819,2823,2827,2833,2837],{"className":2818},[612],[578,2820],{"className":2821,"style":2822},[616],"height:0.8778em;vertical-align:-0.1944em;",[578,2824,2826],{"className":2825},[621],"16",[578,2828,2830],{"className":2829},[621],[578,2831,1693],{"className":2832},[1692],[578,2834,2836],{"className":2835},[621],"9",[578,2838,2840],{"className":2839},[621,1550],[578,2841,2609],{"className":2842},[621],[565,2844,2845,2846,2875,2876,2905,2906,2968,2969,2997],{},"Eine Neuheit spricht sich in einer Stadt mit ",[578,2847,2849,2863],{"className":2848},[581],[578,2850,2852],{"className":2851},[585],[587,2853,2854],{"xmlns":589},[591,2855,2856,2861],{},[594,2857,2858],{},[986,2859,2860],{},"1000",[601,2862,2860],{"encoding":603},[578,2864,2866],{"className":2865,"ariaHidden":608},[607],[578,2867,2869,2872],{"className":2868},[612],[578,2870],{"className":2871,"style":1280},[616],[578,2873,2860],{"className":2874},[621]," möglichen Interessenten herum. Am Anfang kennen sie ",[578,2877,2879,2893],{"className":2878},[581],[578,2880,2882],{"className":2881},[585],[587,2883,2884],{"xmlns":589},[591,2885,2886,2891],{},[594,2887,2888],{},[986,2889,2890],{},"200",[601,2892,2890],{"encoding":603},[578,2894,2896],{"className":2895,"ariaHidden":608},[607],[578,2897,2899,2902],{"className":2898},[612],[578,2900],{"className":2901,"style":1280},[616],[578,2903,2890],{"className":2904},[621],", die Wachstumskonstante ist ",[578,2907,2909,2928],{"className":2908},[581],[578,2910,2912],{"className":2911},[585],[587,2913,2914],{"xmlns":589},[591,2915,2916,2925],{},[594,2917,2918,2920,2922],{},[597,2919,748],{},[640,2921,745],{},[986,2923,2924],{},"0,1",[601,2926,2927],{"encoding":603},"k = 0{,}1",[578,2929,2931,2949],{"className":2930,"ariaHidden":608},[607],[578,2932,2934,2937,2940,2943,2946],{"className":2933},[612],[578,2935],{"className":2936,"style":852},[616],[578,2938,748],{"className":2939,"style":856},[621,622],[578,2941],{"className":2942,"style":838},[675],[578,2944,745],{"className":2945},[842],[578,2947],{"className":2948,"style":838},[675],[578,2950,2952,2955,2958,2964],{"className":2951},[612],[578,2953],{"className":2954,"style":1682},[616],[578,2956,988],{"className":2957},[621],[578,2959,2961],{"className":2960},[621],[578,2962,1693],{"className":2963},[1692],[578,2965,2967],{"className":2966},[621],"1"," pro Tag. Nach ",[578,2970,2972,2985],{"className":2971},[581],[578,2973,2975],{"className":2974},[585],[587,2976,2977],{"xmlns":589},[591,2978,2979,2983],{},[594,2980,2981],{},[986,2982,2069],{},[601,2984,2069],{"encoding":603},[578,2986,2988],{"className":2987,"ariaHidden":608},[607],[578,2989,2991,2994],{"className":2990},[612],[578,2992],{"className":2993,"style":1280},[616],[578,2995,2069],{"className":2996},[621]," Tagen:",[578,2999,3001],{"className":3000},[713],[578,3002,3004,3050],{"className":3003},[581],[578,3005,3007],{"className":3006},[585],[587,3008,3009],{"xmlns":589,"display":722},[591,3010,3011,3047],{},[594,3012,3013,3015,3017,3019,3021,3023,3025,3027,3030,3032,3042,3044],{},[597,3014,645],{},[640,3016,649],{"stretchy":648},[986,3018,2069],{},[640,3020,655],{"stretchy":648},[640,3022,745],{},[986,3024,2860],{},[640,3026,642],{},[986,3028,3029],{},"800",[640,3031,751],{},[728,3033,3034,3036],{},[597,3035,999],{},[594,3037,3038,3040],{},[640,3039,642],{},[986,3041,1806],{},[640,3043,1809],{},[986,3045,3046],{},"514,8",[601,3048,3049],{"encoding":603},"f(5) = 1000 - 800 \\cdot e^{-0{,}5} \\approx 514{,}8",[578,3051,3053,3080,3098,3116,3175],{"className":3052,"ariaHidden":608},[607],[578,3054,3056,3059,3062,3065,3068,3071,3074,3077],{"className":3055},[612],[578,3057],{"className":3058,"style":690},[616],[578,3060,645],{"className":3061,"style":694},[621,622],[578,3063,649],{"className":3064},[698],[578,3066,2069],{"className":3067},[621],[578,3069,655],{"className":3070},[705],[578,3072],{"className":3073,"style":838},[675],[578,3075,745],{"className":3076},[842],[578,3078],{"className":3079,"style":838},[675],[578,3081,3083,3086,3089,3092,3095],{"className":3082},[612],[578,3084],{"className":3085,"style":1862},[616],[578,3087,2860],{"className":3088},[621],[578,3090],{"className":3091,"style":676},[675],[578,3093,642],{"className":3094},[680],[578,3096],{"className":3097,"style":676},[675],[578,3099,3101,3104,3107,3110,3113],{"className":3100},[612],[578,3102],{"className":3103,"style":1280},[616],[578,3105,3029],{"className":3106},[621],[578,3108],{"className":3109,"style":676},[675],[578,3111,751],{"className":3112},[680],[578,3114],{"className":3115,"style":676},[675],[578,3117,3119,3122,3166,3169,3172],{"className":3118},[612],[578,3120],{"className":3121,"style":1923},[616],[578,3123,3125,3128],{"className":3124},[621],[578,3126,999],{"className":3127},[621,622],[578,3129,3131],{"className":3130},[791],[578,3132,3134],{"className":3133},[795],[578,3135,3137],{"className":3136},[799],[578,3138,3140],{"className":3139,"style":1923},[803],[578,3141,3142,3145],{"style":807},[578,3143],{"className":3144,"style":812},[811],[578,3146,3148],{"className":3147},[816,817,818,819],[578,3149,3151,3154,3157,3163],{"className":3150},[621,819],[578,3152,642],{"className":3153},[621,819],[578,3155,988],{"className":3156},[621,819],[578,3158,3160],{"className":3159},[621,819],[578,3161,1693],{"className":3162},[1692,819],[578,3164,2069],{"className":3165},[621,819],[578,3167],{"className":3168,"style":838},[675],[578,3170,1809],{"className":3171},[842],[578,3173],{"className":3174,"style":838},[675],[578,3176,3178,3181,3185,3191],{"className":3177},[612],[578,3179],{"className":3180,"style":1682},[616],[578,3182,3184],{"className":3183},[621],"514",[578,3186,3188],{"className":3187},[621],[578,3189,1693],{"className":3190},[1692],[578,3192,3194],{"className":3193},[621],"8",[560,3196,3198],{"id":3197},"typische-fehler","Typische Fehler",[3200,3201,3202,3519,3621],"ul",{},[3203,3204,3205,3206,3294,3295,3361,3362,3518],"li",{},"Den Faktor vor der e-Funktion falsch wählen: Es ist ",[578,3207,3209,3237],{"className":3208},[581],[578,3210,3212],{"className":3211},[585],[587,3213,3214],{"xmlns":589},[591,3215,3216,3234],{},[594,3217,3218,3220,3222,3224,3226,3228,3230,3232],{},[597,3219,599],{},[640,3221,642],{},[597,3223,645],{},[640,3225,649],{"stretchy":648},[986,3227,988],{},[640,3229,655],{"stretchy":648},[640,3231,745],{},[986,3233,3029],{},[601,3235,3236],{"encoding":603},"S - f(0) = 800",[578,3238,3240,3258,3285],{"className":3239,"ariaHidden":608},[607],[578,3241,3243,3246,3249,3252,3255],{"className":3242},[612],[578,3244],{"className":3245,"style":668},[616],[578,3247,599],{"className":3248,"style":623},[621,622],[578,3250],{"className":3251,"style":676},[675],[578,3253,642],{"className":3254},[680],[578,3256],{"className":3257,"style":676},[675],[578,3259,3261,3264,3267,3270,3273,3276,3279,3282],{"className":3260},[612],[578,3262],{"className":3263,"style":690},[616],[578,3265,645],{"className":3266,"style":694},[621,622],[578,3268,649],{"className":3269},[698],[578,3271,988],{"className":3272},[621],[578,3274,655],{"className":3275},[705],[578,3277],{"className":3278,"style":838},[675],[578,3280,745],{"className":3281},[842],[578,3283],{"className":3284,"style":838},[675],[578,3286,3288,3291],{"className":3287},[612],[578,3289],{"className":3290,"style":1280},[616],[578,3292,3029],{"className":3293},[621],", nicht ",[578,3296,3298,3322],{"className":3297},[581],[578,3299,3301],{"className":3300},[585],[587,3302,3303],{"xmlns":589},[591,3304,3305,3319],{},[594,3306,3307,3309,3311,3313,3315,3317],{},[597,3308,645],{},[640,3310,649],{"stretchy":648},[986,3312,988],{},[640,3314,655],{"stretchy":648},[640,3316,745],{},[986,3318,2890],{},[601,3320,3321],{"encoding":603},"f(0) = 200",[578,3323,3325,3352],{"className":3324,"ariaHidden":608},[607],[578,3326,3328,3331,3334,3337,3340,3343,3346,3349],{"className":3327},[612],[578,3329],{"className":3330,"style":690},[616],[578,3332,645],{"className":3333,"style":694},[621,622],[578,3335,649],{"className":3336},[698],[578,3338,988],{"className":3339},[621],[578,3341,655],{"className":3342},[705],[578,3344],{"className":3345,"style":838},[675],[578,3347,745],{"className":3348},[842],[578,3350],{"className":3351,"style":838},[675],[578,3353,3355,3358],{"className":3354},[612],[578,3356],{"className":3357,"style":1280},[616],[578,3359,2890],{"className":3360},[621],". Mit ",[578,3363,3365,3400],{"className":3364},[581],[578,3366,3368],{"className":3367},[585],[587,3369,3370],{"xmlns":589},[591,3371,3372,3397],{},[594,3373,3374,3376,3378,3380,3382,3392,3394],{},[986,3375,2860],{},[640,3377,642],{},[986,3379,2890],{},[640,3381,751],{},[728,3383,3384,3386],{},[597,3385,999],{},[594,3387,3388,3390],{},[640,3389,642],{},[986,3391,1806],{},[640,3393,1809],{},[986,3395,3396],{},"878,7",[601,3398,3399],{"encoding":603},"1000 - 200 \\cdot e^{-0{,}5} \\approx 878{,}7",[578,3401,3403,3421,3439,3498],{"className":3402,"ariaHidden":608},[607],[578,3404,3406,3409,3412,3415,3418],{"className":3405},[612],[578,3407],{"className":3408,"style":1862},[616],[578,3410,2860],{"className":3411},[621],[578,3413],{"className":3414,"style":676},[675],[578,3416,642],{"className":3417},[680],[578,3419],{"className":3420,"style":676},[675],[578,3422,3424,3427,3430,3433,3436],{"className":3423},[612],[578,3425],{"className":3426,"style":1280},[616],[578,3428,2890],{"className":3429},[621],[578,3431],{"className":3432,"style":676},[675],[578,3434,751],{"className":3435},[680],[578,3437],{"className":3438,"style":676},[675],[578,3440,3442,3445,3489,3492,3495],{"className":3441},[612],[578,3443],{"className":3444,"style":2302},[616],[578,3446,3448,3451],{"className":3447},[621],[578,3449,999],{"className":3450},[621,622],[578,3452,3454],{"className":3453},[791],[578,3455,3457],{"className":3456},[795],[578,3458,3460],{"className":3459},[799],[578,3461,3463],{"className":3462,"style":2302},[803],[578,3464,3465,3468],{"style":1143},[578,3466],{"className":3467,"style":812},[811],[578,3469,3471],{"className":3470},[816,817,818,819],[578,3472,3474,3477,3480,3486],{"className":3473},[621,819],[578,3475,642],{"className":3476},[621,819],[578,3478,988],{"className":3479},[621,819],[578,3481,3483],{"className":3482},[621,819],[578,3484,1693],{"className":3485},[1692,819],[578,3487,2069],{"className":3488},[621,819],[578,3490],{"className":3491,"style":838},[675],[578,3493,1809],{"className":3494},[842],[578,3496],{"className":3497,"style":838},[675],[578,3499,3501,3504,3508,3514],{"className":3500},[612],[578,3502],{"className":3503,"style":1682},[616],[578,3505,3507],{"className":3506},[621],"878",[578,3509,3511],{"className":3510},[621],[578,3512,1693],{"className":3513},[1692],[578,3515,3517],{"className":3516},[621],"7"," stimmt nicht einmal der Startwert.",[3203,3520,3521,3522,3591,3592,3620],{},"Das Minus im Exponenten vergessen: 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wächst über alle Grenzen, der Bestand würde sich nicht an ",[578,3593,3595,3608],{"className":3594},[581],[578,3596,3598],{"className":3597},[585],[587,3599,3600],{"xmlns":589},[591,3601,3602,3606],{},[594,3603,3604],{},[597,3605,599],{},[601,3607,599],{"encoding":603},[578,3609,3611],{"className":3610,"ariaHidden":608},[607],[578,3612,3614,3617],{"className":3613},[612],[578,3615],{"className":3616,"style":617},[616],[578,3618,599],{"className":3619,"style":623},[621,622]," annähern.",[3203,3622,3623],{},"Beschränktes und logistisches Wachstum verwechseln: Beim beschränkten Wachstum ist die Zunahme am Anfang am größten, der Graph hat keinen Wendepunkt.",{"title":3625,"searchDepth":3626,"depth":3626,"links":3627},"",2,[3628,3629,3630],{"id":562,"depth":3626,"text":563},{"id":1465,"depth":3626,"text":1466},{"id":3197,"depth":3626,"text":3198},[3632,3635,3638,3641,3649,3652,3654,3657,3665],{"lhs":3633,"rhs":3634},"S - (S - f0)*e^(-k*0)","f0",{"lhs":3636,"rhs":3637},"k*(S - 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