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Das ist zur Zeit ",[575,1126,1128,1192],{"className":1127},[578],[575,1129,1131],{"className":1130},[582],[584,1132,1133],{"xmlns":586},[588,1134,1135,1189],{},[591,1136,1137,1145,1147],{},[1138,1139,1140,1142],"msub",{},[594,1141,657],{},[594,1143,1144],{},"W",[646,1146,663],{},[996,1148,1149,1183],{},[591,1150,1151,1154,1157],{},[594,1152,1153],{},"ln",[646,1155,1156],{},"⁡",[591,1158,1159,1161,1176,1178,1181],{},[646,1160,654],{"fence":605},[996,1162,1163,1165],{},[594,1164,596],{},[591,1166,1167,1169,1171,1174],{},[594,1168,644],{},[646,1170,654],{"stretchy":653},[1001,1172,1173],{},"0",[646,1175,660],{"stretchy":653},[646,1177,687],{},[1001,1179,1180],{},"1",[646,1182,660],{"fence":605},[591,1184,1185,1187],{},[594,1186,666],{},[594,1188,596],{},[598,1190,1191],{"encoding":600},"t_W = \\frac{\\ln\\left(\\frac{S}{f(0)} - 1\\right)}{kS}",[575,1193,1195,1255],{"className":1194,"ariaHidden":605},[604],[575,1196,1198,1202,1246,1249,1252],{"className":1197},[609],[575,1199],{"className":1200,"style":1201},[613],"height:0.7651em;vertical-align:-0.15em;",[575,1203,1205,1208],{"className":1204},[618],[575,1206,657],{"className":1207},[618,619],[575,1209,1211],{"className":1210},[721],[575,1212,1214,1237],{"className":1213},[725,1057],[575,1215,1217,1234],{"className":1216},[729],[575,1218,1221],{"className":1219,"style":1220},[733],"height:0.3283em;",[575,1222,1224,1227],{"style":1223},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[575,1225],{"className":1226,"style":742},[741],[575,1228,1230],{"className":1229},[746,747,748,749],[575,1231,1144],{"className":1232,"style":1233},[618,619,749],"margin-right:0.1389em;",[575,1235,1111],{"className":1236},[1110],[575,1238,1240],{"className":1239},[729],[575,1241,1244],{"className":1242,"style":1243},[733],"height:0.15em;",[575,1245],{},[575,1247],{"className":1248,"style":771},[770],[575,1250,663],{"className":1251},[775],[575,1253],{"className":1254,"style":771},[770],[575,1256,1258,1262],{"className":1257},[609],[575,1259],{"className":1260,"style":1261},[613],"height:1.7289em;vertical-align:-0.345em;",[575,1263,1265,1268,1450],{"className":1264},[618],[575,1266],{"className":1267},[759,1050],[575,1269,1271],{"className":1270},[996],[575,1272,1274,1442],{"className":1273},[725,1057],[575,1275,1277,1439],{"className":1276},[729],[575,1278,1281,1298,1306],{"className":1279,"style":1280},[733],"height:1.384em;",[575,1282,1283,1286],{"style":1067},[575,1284],{"className":1285,"style":1071},[741],[575,1287,1289],{"className":1288},[746,747,748,749],[575,1290,1292,1295],{"className":1291},[618,749],[575,1293,666],{"className":1294,"style":789},[618,619,749],[575,1296,596],{"className":1297,"style":620},[618,619,749],[575,1299,1300,1303],{"style":1083},[575,1301],{"className":1302,"style":1071},[741],[575,1304],{"className":1305,"style":1091},[1090],[575,1307,1309,1312],{"style":1308},"top:-3.6865em;",[575,1310],{"className":1311,"style":1071},[741],[575,1313,1315],{"className":1314},[746,747,748,749],[575,1316,1318,1330],{"className":1317},[618,749],[575,1319,1322,1326],{"className":1320},[1321,749],"mop",[575,1323,1325],{"className":1324},[749],"l",[575,1327,1329],{"className":1328},[749],"n",[575,1331,1334,1344,1427,1430,1433],{"className":1332},[1333,749],"minner",[575,1335,1341],{"className":1336,"style":1340},[759,746,1337,1338,749,1339],"reset-size3","size6","delimcenter","top:0.075em;",[575,1342,654],{"className":1343},[749],[575,1345,1347,1350,1424],{"className":1346},[618,749],[575,1348],{"className":1349},[759,1050,746,1337,1338],[575,1351,1353],{"className":1352},[996],[575,1354,1356,1415],{"className":1355},[725,1057],[575,1357,1359,1412],{"className":1358},[729],[575,1360,1363,1387,1397],{"className":1361,"style":1362},[733],"height:0.8721em;",[575,1364,1366,1369],{"style":1365},"top:-2.6408em;",[575,1367],{"className":1368,"style":1071},[741],[575,1370,1372],{"className":1371},[746,1337,843,749],[575,1373,1375,1378,1381,1384],{"className":1374},[618,749],[575,1376,644],{"className":1377,"style":717},[618,619,749],[575,1379,654],{"className":1380},[759,749],[575,1382,1173],{"className":1383},[618,749],[575,1385,660],{"className":1386},[766,749],[575,1388,1390,1393],{"style":1389},"top:-3.2255em;",[575,1391],{"className":1392,"style":1071},[741],[575,1394],{"className":1395,"style":1396},[1090,749],"border-bottom-width:0.049em;",[575,1398,1400,1403],{"style":1399},"top:-3.384em;",[575,1401],{"className":1402,"style":1071},[741],[575,1404,1406],{"className":1405},[746,1337,843,749],[575,1407,1409],{"className":1408},[618,749],[575,1410,596],{"className":1411,"style":620},[618,619,749],[575,1413,1111],{"className":1414},[1110],[575,1416,1418],{"className":1417},[729],[575,1419,1422],{"className":1420,"style":1421},[733],"height:0.5378em;",[575,1423],{},[575,1425],{"className":1426},[766,1050,746,1337,1338],[575,1428,687],{"className":1429},[797,749],[575,1431,1180],{"className":1432},[618,749],[575,1434,1436],{"className":1435,"style":1340},[766,746,1337,1338,749,1339],[575,1437,660],{"className":1438},[749],[575,1440,1111],{"className":1441},[1110],[575,1443,1445],{"className":1444},[729],[575,1446,1448],{"className":1447,"style":1118},[733],[575,1449],{},[575,1451],{"className":1452},[766,1050],".",[889,1455,1456,1457,1485],{},"Danach nähert sich der Bestand der Schranke ",[575,1458,1460,1473],{"className":1459},[578],[575,1461,1463],{"className":1462},[582],[584,1464,1465],{"xmlns":586},[588,1466,1467,1471],{},[591,1468,1469],{},[594,1470,596],{},[598,1472,596],{"encoding":600},[575,1474,1476],{"className":1475,"ariaHidden":605},[604],[575,1477,1479,1482],{"className":1478},[609],[575,1480],{"className":1481,"style":614},[613],[575,1483,596],{"className":1484,"style":620},[618,619],", erreicht sie aber nie.",[564,1487,1488,1489,1531,1532,1589,1590,1618,1619,1871,1872,1939,1940,1974],{},"Manche Bücher schreiben den Exponenten als ",[575,1490,1492,1511],{"className":1491},[578],[575,1493,1495],{"className":1494},[582],[584,1496,1497],{"xmlns":586},[588,1498,1499,1508],{},[591,1500,1501,1503,1506],{},[646,1502,687],{},[594,1504,1505],{},"r",[594,1507,657],{},[598,1509,1510],{"encoding":600},"-rt",[575,1512,1514],{"className":1513,"ariaHidden":605},[604],[575,1515,1517,1521,1524,1528],{"className":1516},[609],[575,1518],{"className":1519,"style":1520},[613],"height:0.6984em;vertical-align:-0.0833em;",[575,1522,687],{"className":1523},[618],[575,1525,1505],{"className":1526,"style":1527},[618,619],"margin-right:0.0278em;",[575,1529,657],{"className":1530},[618,619]," mit ",[575,1533,1535,1555],{"className":1534},[578],[575,1536,1538],{"className":1537},[582],[584,1539,1540],{"xmlns":586},[588,1541,1542,1552],{},[591,1543,1544,1546,1548,1550],{},[594,1545,1505],{},[646,1547,663],{},[594,1549,666],{},[594,1551,596],{},[598,1553,1554],{"encoding":600},"r = kS",[575,1556,1558,1577],{"className":1557,"ariaHidden":605},[604],[575,1559,1561,1565,1568,1571,1574],{"className":1560},[609],[575,1562],{"className":1563,"style":1564},[613],"height:0.4306em;",[575,1566,1505],{"className":1567,"style":1527},[618,619],[575,1569],{"className":1570,"style":771},[770],[575,1572,663],{"className":1573},[775],[575,1575],{"className":1576,"style":771},[770],[575,1578,1580,1583,1586],{"className":1579},[609],[575,1581],{"className":1582,"style":785},[613],[575,1584,666],{"className":1585,"style":789},[618,619],[575,1587,596],{"className":1588,"style":620},[618,619],". Dann ist ",[575,1591,1593,1606],{"className":1592},[578],[575,1594,1596],{"className":1595},[582],[584,1597,1598],{"xmlns":586},[588,1599,1600,1604],{},[591,1601,1602],{},[594,1603,1505],{},[598,1605,1505],{"encoding":600},[575,1607,1609],{"className":1608,"ariaHidden":605},[604],[575,1610,1612,1615],{"className":1611},[609],[575,1613],{"className":1614,"style":1564},[613],[575,1616,1505],{"className":1617,"style":1527},[618,619]," näherungsweise die anfängliche Wachstumsrate (genau gilt ",[575,1620,1622,1684],{"className":1621},[578],[575,1623,1625],{"className":1624},[582],[584,1626,1627],{"xmlns":586},[588,1628,1629,1681],{},[591,1630,1631,1657,1659,1661,1665,1667,1669,1671,1673,1675,1677,1679],{},[996,1632,1633,1647],{},[591,1634,1635,1641,1643,1645],{},[640,1636,1637,1639],{},[594,1638,644],{},[646,1640,650],{"mathvariant":648,"lspace":649,"rspace":649},[646,1642,654],{"stretchy":653},[1001,1644,1173],{},[646,1646,660],{"stretchy":653},[591,1648,1649,1651,1653,1655],{},[594,1650,644],{},[646,1652,654],{"stretchy":653},[1001,1654,1173],{},[646,1656,660],{"stretchy":653},[646,1658,663],{},[594,1660,666],{},[1662,1663,1664],"mtext",{}," ",[646,1666,654],{"stretchy":653},[594,1668,596],{},[646,1670,687],{},[594,1672,644],{},[646,1674,654],{"stretchy":653},[1001,1676,1173],{},[646,1678,660],{"stretchy":653},[646,1680,660],{"stretchy":653},[598,1682,1683],{"encoding":600},"\\frac{f'(0)}{f(0)} = k\\,(S - f(0))",[575,1685,1687,1824,1852],{"className":1686,"ariaHidden":605},[604],[575,1688,1690,1694,1815,1818,1821],{"className":1689},[609],[575,1691],{"className":1692,"style":1693},[613],"height:1.5845em;vertical-align:-0.52em;",[575,1695,1697,1700,1812],{"className":1696},[618],[575,1698],{"className":1699},[759,1050],[575,1701,1703],{"className":1702},[996],[575,1704,1706,1803],{"className":1705},[725,1057],[575,1707,1709,1800],{"className":1708},[729],[575,1710,1713,1736,1744],{"className":1711,"style":1712},[733],"height:1.0645em;",[575,1714,1715,1718],{"style":1067},[575,1716],{"className":1717,"style":1071},[741],[575,1719,1721],{"className":1720},[746,747,748,749],[575,1722,1724,1727,1730,1733],{"className":1723},[618,749],[575,1725,644],{"className":1726,"style":717},[618,619,749],[575,1728,654],{"className":1729},[759,749],[575,1731,1173],{"className":1732},[618,749],[575,1734,660],{"className":1735},[766,749],[575,1737,1738,1741],{"style":1083},[575,1739],{"className":1740,"style":1071},[741],[575,1742],{"className":1743,"style":1091},[1090],[575,1745,1747,1750],{"style":1746},"top:-3.485em;",[575,1748],{"className":1749,"style":1071},[741],[575,1751,1753],{"className":1752},[746,747,748,749],[575,1754,1756,1791,1794,1797],{"className":1755},[618,749],[575,1757,1759,1762],{"className":1758},[618,749],[575,1760,644],{"className":1761,"style":717},[618,619,749],[575,1763,1765],{"className":1764},[721],[575,1766,1768],{"className":1767},[725],[575,1769,1771],{"className":1770},[729],[575,1772,1775],{"className":1773,"style":1774},[733],"height:0.8278em;",[575,1776,1778,1782],{"style":1777},"top:-2.931em;margin-right:0.0714em;",[575,1779],{"className":1780,"style":1781},[741],"height:2.5em;",[575,1783,1785],{"className":1784},[746,1337,843,749],[575,1786,1788],{"className":1787},[618,749],[575,1789,650],{"className":1790},[618,749],[575,1792,654],{"className":1793},[759,749],[575,1795,1173],{"className":1796},[618,749],[575,1798,660],{"className":1799},[766,749],[575,1801,1111],{"className":1802},[1110],[575,1804,1806],{"className":1805},[729],[575,1807,1810],{"className":1808,"style":1809},[733],"height:0.52em;",[575,1811],{},[575,1813],{"className":1814},[766,1050],[575,1816],{"className":1817,"style":771},[770],[575,1819,663],{"className":1820},[775],[575,1822],{"className":1823,"style":771},[770],[575,1825,1827,1830,1833,1837,1840,1843,1846,1849],{"className":1826},[609],[575,1828],{"className":1829,"style":807},[613],[575,1831,666],{"className":1832,"style":789},[618,619],[575,1834],{"className":1835,"style":1836},[770],"margin-right:0.1667em;",[575,1838,654],{"className":1839},[759],[575,1841,596],{"className":1842,"style":620},[618,619],[575,1844],{"className":1845,"style":793},[770],[575,1847,687],{"className":1848},[797],[575,1850],{"className":1851,"style":793},[770],[575,1853,1855,1858,1861,1864,1867],{"className":1854},[609],[575,1856],{"className":1857,"style":807},[613],[575,1859,644],{"className":1860,"style":717},[618,619],[575,1862,654],{"className":1863},[759],[575,1865,1173],{"className":1866},[618],[575,1868,1870],{"className":1869},[766],"))",", und das ist nur für ",[575,1873,1875,1900],{"className":1874},[578],[575,1876,1878],{"className":1877},[582],[584,1879,1880],{"xmlns":586},[588,1881,1882,1897],{},[591,1883,1884,1886,1888,1890,1892,1895],{},[594,1885,644],{},[646,1887,654],{"stretchy":653},[1001,1889,1173],{},[646,1891,660],{"stretchy":653},[646,1893,1894],{},"≪",[594,1896,596],{},[598,1898,1899],{"encoding":600},"f(0) \\ll S",[575,1901,1903,1930],{"className":1902,"ariaHidden":605},[604],[575,1904,1906,1909,1912,1915,1918,1921,1924,1927],{"className":1905},[609],[575,1907],{"className":1908,"style":807},[613],[575,1910,644],{"className":1911,"style":717},[618,619],[575,1913,654],{"className":1914},[759],[575,1916,1173],{"className":1917},[618],[575,1919,660],{"className":1920},[766],[575,1922],{"className":1923,"style":771},[770],[575,1925,1894],{"className":1926},[775],[575,1928],{"className":1929,"style":771},[770],[575,1931,1933,1936],{"className":1932},[609],[575,1934],{"className":1935,"style":614},[613],[575,1937,596],{"className":1938,"style":620},[618,619]," etwa ",[575,1941,1943,1959],{"className":1942},[578],[575,1944,1946],{"className":1945},[582],[584,1947,1948],{"xmlns":586},[588,1949,1950,1956],{},[591,1951,1952,1954],{},[594,1953,666],{},[594,1955,596],{},[598,1957,1958],{"encoding":600},"kS",[575,1960,1962],{"className":1961,"ariaHidden":605},[604],[575,1963,1965,1968,1971],{"className":1964},[609],[575,1966],{"className":1967,"style":785},[613],[575,1969,666],{"className":1970,"style":789},[618,619],[575,1972,596],{"className":1973,"style":620},[618,619],"). Vor dem Rechnen sollte man prüfen, welche Schreibweise eine Aufgabe verwendet.",[559,1976,1978],{"id":1977},"beispiele","Beispiele",[564,1980,1981,1982,2012,2013,2042,2043,972,2108,2175,2176,2337,2338,2367],{},"Auf einer Insel leben ",[575,1983,1985,1999],{"className":1984},[578],[575,1986,1988],{"className":1987},[582],[584,1989,1990],{"xmlns":586},[588,1991,1992,1997],{},[591,1993,1994],{},[1001,1995,1996],{},"50",[598,1998,1996],{"encoding":600},[575,2000,2002],{"className":2001,"ariaHidden":605},[604],[575,2003,2005,2009],{"className":2004},[609],[575,2006],{"className":2007,"style":2008},[613],"height:0.6444em;",[575,2010,1996],{"className":2011},[618]," Kaninchen, Platz ist für höchstens ",[575,2014,2016,2030],{"className":2015},[578],[575,2017,2019],{"className":2018},[582],[584,2020,2021],{"xmlns":586},[588,2022,2023,2028],{},[591,2024,2025],{},[1001,2026,2027],{},"1000",[598,2029,2027],{"encoding":600},[575,2031,2033],{"className":2032,"ariaHidden":605},[604],[575,2034,2036,2039],{"className":2035},[609],[575,2037],{"className":2038,"style":2008},[613],[575,2040,2027],{"className":2041},[618],". Mit ",[575,2044,2046,2065],{"className":2045},[578],[575,2047,2049],{"className":2048},[582],[584,2050,2051],{"xmlns":586},[588,2052,2053,2062],{},[591,2054,2055,2057,2059],{},[594,2056,666],{},[646,2058,663],{},[1001,2060,2061],{},"0,0004",[598,2063,2064],{"encoding":600},"k = 0{,}0004",[575,2066,2068,2086],{"className":2067,"ariaHidden":605},[604],[575,2069,2071,2074,2077,2080,2083],{"className":2070},[609],[575,2072],{"className":2073,"style":785},[613],[575,2075,666],{"className":2076,"style":789},[618,619],[575,2078],{"className":2079,"style":771},[770],[575,2081,663],{"className":2082},[775],[575,2084],{"className":2085,"style":771},[770],[575,2087,2089,2093,2096,2104],{"className":2088},[609],[575,2090],{"className":2091,"style":2092},[613],"height:0.8389em;vertical-align:-0.1944em;",[575,2094,1173],{"className":2095},[618],[575,2097,2099],{"className":2098},[618],[575,2100,2103],{"className":2101},[2102],"mpunct",",",[575,2105,2107],{"className":2106},[618],"0004",[575,2109,2111,2132],{"className":2110},[578],[575,2112,2114],{"className":2113},[582],[584,2115,2116],{"xmlns":586},[588,2117,2118,2129],{},[591,2119,2120,2122,2124,2126],{},[594,2121,666],{},[594,2123,596],{},[646,2125,663],{},[1001,2127,2128],{},"0,4",[598,2130,2131],{"encoding":600},"kS = 0{,}4",[575,2133,2135,2156],{"className":2134,"ariaHidden":605},[604],[575,2136,2138,2141,2144,2147,2150,2153],{"className":2137},[609],[575,2139],{"className":2140,"style":785},[613],[575,2142,666],{"className":2143,"style":789},[618,619],[575,2145,596],{"className":2146,"style":620},[618,619],[575,2148],{"className":2149,"style":771},[770],[575,2151,663],{"className":2152},[775],[575,2154],{"className":2155,"style":771},[770],[575,2157,2159,2162,2165,2171],{"className":2158},[609],[575,2160],{"className":2161,"style":2092},[613],[575,2163,1173],{"className":2164},[618],[575,2166,2168],{"className":2167},[618],[575,2169,2103],{"className":2170},[2102],[575,2172,2174],{"className":2173},[618],"4"," pro Jahr, und ",[575,2177,2179,2214],{"className":2178},[578],[575,2180,2182],{"className":2181},[582],[584,2183,2184],{"xmlns":586},[588,2185,2186,2211],{},[591,2187,2188,2202,2204,2206,2208],{},[996,2189,2190,2192],{},[594,2191,596],{},[591,2193,2194,2196,2198,2200],{},[594,2195,644],{},[646,2197,654],{"stretchy":653},[1001,2199,1173],{},[646,2201,660],{"stretchy":653},[646,2203,687],{},[1001,2205,1180],{},[646,2207,663],{},[1001,2209,2210],{},"19",[598,2212,2213],{"encoding":600},"\\frac{S}{f(0)} - 1 = 19",[575,2215,2217,2310,2328],{"className":2216,"ariaHidden":605},[604],[575,2218,2220,2224,2301,2304,2307],{"className":2219},[609],[575,2221],{"className":2222,"style":2223},[613],"height:1.3923em;vertical-align:-0.52em;",[575,2225,2227,2230,2298],{"className":2226},[618],[575,2228],{"className":2229},[759,1050],[575,2231,2233],{"className":2232},[996],[575,2234,2236,2290],{"className":2235},[725,1057],[575,2237,2239,2287],{"className":2238},[729],[575,2240,2242,2265,2273],{"className":2241,"style":1064},[733],[575,2243,2244,2247],{"style":1067},[575,2245],{"className":2246,"style":1071},[741],[575,2248,2250],{"className":2249},[746,747,748,749],[575,2251,2253,2256,2259,2262],{"className":2252},[618,749],[575,2254,644],{"className":2255,"style":717},[618,619,749],[575,2257,654],{"className":2258},[759,749],[575,2260,1173],{"className":2261},[618,749],[575,2263,660],{"className":2264},[766,749],[575,2266,2267,2270],{"style":1083},[575,2268],{"className":2269,"style":1071},[741],[575,2271],{"className":2272,"style":1091},[1090],[575,2274,2275,2278],{"style":1094},[575,2276],{"className":2277,"style":1071},[741],[575,2279,2281],{"className":2280},[746,747,748,749],[575,2282,2284],{"className":2283},[618,749],[575,2285,596],{"className":2286,"style":620},[618,619,749],[575,2288,1111],{"className":2289},[1110],[575,2291,2293],{"className":2292},[729],[575,2294,2296],{"className":2295,"style":1809},[733],[575,2297],{},[575,2299],{"className":2300},[766,1050],[575,2302],{"className":2303,"style":793},[770],[575,2305,687],{"className":2306},[797],[575,2308],{"className":2309,"style":793},[770],[575,2311,2313,2316,2319,2322,2325],{"className":2312},[609],[575,2314],{"className":2315,"style":2008},[613],[575,2317,1180],{"className":2318},[618],[575,2320],{"className":2321,"style":771},[770],[575,2323,663],{"className":2324},[775],[575,2326],{"className":2327,"style":771},[770],[575,2329,2331,2334],{"className":2330},[609],[575,2332],{"className":2333,"style":2008},[613],[575,2335,2210],{"className":2336},[618],". Nach ",[575,2339,2341,2355],{"className":2340},[578],[575,2342,2344],{"className":2343},[582],[584,2345,2346],{"xmlns":586},[588,2347,2348,2353],{},[591,2349,2350],{},[1001,2351,2352],{},"5",[598,2354,2352],{"encoding":600},[575,2356,2358],{"className":2357,"ariaHidden":605},[604],[575,2359,2361,2364],{"className":2360},[609],[575,2362],{"className":2363,"style":2008},[613],[575,2365,2352],{"className":2366},[618]," Jahren:",[575,2369,2371],{"className":2370},[625],[575,2372,2374,2458],{"className":2373},[578],[575,2375,2377],{"className":2376},[582],[584,2378,2379],{"xmlns":586,"display":634},[588,2380,2381,2455],{},[591,2382,2383,2385,2387,2389,2391,2393,2423,2425,2449,2452],{},[594,2384,644],{},[646,2386,654],{"stretchy":653},[1001,2388,2352],{},[646,2390,660],{"stretchy":653},[646,2392,663],{},[996,2394,2395,2397],{},[1001,2396,2027],{},[591,2398,2399,2401,2404,2406,2408],{},[1001,2400,1180],{},[646,2402,2403],{},"+",[1001,2405,2210],{},[646,2407,669],{},[640,2409,2410,2413],{},[594,2411,2412],{},"e",[591,2414,2415,2417,2419,2421],{},[646,2416,687],{},[1001,2418,2128],{},[646,2420,669],{},[1001,2422,2352],{},[646,2424,663],{},[996,2426,2427,2429],{},[1001,2428,2027],{},[591,2430,2431,2433,2435,2437,2439],{},[1001,2432,1180],{},[646,2434,2403],{},[1001,2436,2210],{},[646,2438,669],{},[640,2440,2441,2443],{},[594,2442,2412],{},[591,2444,2445,2447],{},[646,2446,687],{},[1001,2448,1003],{},[646,2450,2451],{},"≈",[1001,2453,2454],{},"280",[598,2456,2457],{"encoding":600},"f(5) = \\frac{1000}{1 + 19 \\cdot e^{-0{,}4 \\cdot 5}} = \\frac{1000}{1 + 19 \\cdot e^{-2}} \\approx 280",[575,2459,2461,2488,2643,2776],{"className":2460,"ariaHidden":605},[604],[575,2462,2464,2467,2470,2473,2476,2479,2482,2485],{"className":2463},[609],[575,2465],{"className":2466,"style":807},[613],[575,2468,644],{"className":2469,"style":717},[618,619],[575,2471,654],{"className":2472},[759],[575,2474,2352],{"className":2475},[618],[575,2477,660],{"className":2478},[766],[575,2480],{"className":2481,"style":771},[770],[575,2483,663],{"className":2484},[775],[575,2486],{"className":2487,"style":771},[770],[575,2489,2491,2495,2634,2637,2640],{"className":2490},[609],[575,2492],{"className":2493,"style":2494},[613],"height:2.0908em;vertical-align:-0.7693em;",[575,2496,2498,2501,2631],{"className":2497},[618],[575,2499],{"className":2500},[759,1050],[575,2502,2504],{"className":2503},[996],[575,2505,2507,2622],{"className":2506},[725,1057],[575,2508,2510,2619],{"className":2509},[729],[575,2511,2514,2599,2607],{"className":2512,"style":2513},[733],"height:1.3214em;",[575,2515,2517,2520],{"style":2516},"top:-2.314em;",[575,2518],{"className":2519,"style":1071},[741],[575,2521,2523,2526,2529,2532,2535,2538,2541,2544,2547],{"className":2522},[618],[575,2524,1180],{"className":2525},[618],[575,2527],{"className":2528,"style":793},[770],[575,2530,2403],{"className":2531},[797],[575,2533],{"className":2534,"style":793},[770],[575,2536,2210],{"className":2537},[618],[575,2539],{"className":2540,"style":793},[770],[575,2542,669],{"className":2543},[797],[575,2545],{"className":2546,"style":793},[770],[575,2548,2550,2553],{"className":2549},[618],[575,2551,2412],{"className":2552},[618,619],[575,2554,2556],{"className":2555},[721],[575,2557,2559],{"className":2558},[725],[575,2560,2562],{"className":2561},[729],[575,2563,2566],{"className":2564,"style":2565},[733],"height:0.7401em;",[575,2567,2569,2572],{"style":2568},"top:-2.989em;margin-right:0.05em;",[575,2570],{"className":2571,"style":742},[741],[575,2573,2575],{"className":2574},[746,747,748,749],[575,2576,2578,2581,2584,2590,2593,2596],{"className":2577},[618,749],[575,2579,687],{"className":2580},[618,749],[575,2582,1173],{"className":2583},[618,749],[575,2585,2587],{"className":2586},[618,749],[575,2588,2103],{"className":2589},[2102,749],[575,2591,2174],{"className":2592},[618,749],[575,2594,669],{"className":2595},[797,749],[575,2597,2352],{"className":2598},[618,749],[575,2600,2601,2604],{"style":1083},[575,2602],{"className":2603,"style":1071},[741],[575,2605],{"className":2606,"style":1091},[1090],[575,2608,2610,2613],{"style":2609},"top:-3.677em;",[575,2611],{"className":2612,"style":1071},[741],[575,2614,2616],{"className":2615},[618],[575,2617,2027],{"className":2618},[618],[575,2620,1111],{"className":2621},[1110],[575,2623,2625],{"className":2624},[729],[575,2626,2629],{"className":2627,"style":2628},[733],"height:0.7693em;",[575,2630],{},[575,2632],{"className":2633},[766,1050],[575,2635],{"className":2636,"style":771},[770],[575,2638,663],{"className":2639},[775],[575,2641],{"className":2642,"style":771},[770],[575,2644,2646,2649,2767,2770,2773],{"className":2645},[609],[575,2647],{"className":2648,"style":2494},[613],[575,2650,2652,2655,2764],{"className":2651},[618],[575,2653],{"className":2654},[759,1050],[575,2656,2658],{"className":2657},[996],[575,2659,2661,2756],{"className":2660},[725,1057],[575,2662,2664,2753],{"className":2663},[729],[575,2665,2667,2734,2742],{"className":2666,"style":2513},[733],[575,2668,2669,2672],{"style":2516},[575,2670],{"className":2671,"style":1071},[741],[575,2673,2675,2678,2681,2684,2687,2690,2693,2696,2699],{"className":2674},[618],[575,2676,1180],{"className":2677},[618],[575,2679],{"className":2680,"style":793},[770],[575,2682,2403],{"className":2683},[797],[575,2685],{"className":2686,"style":793},[770],[575,2688,2210],{"className":2689},[618],[575,2691],{"className":2692,"style":793},[770],[575,2694,669],{"className":2695},[797],[575,2697],{"className":2698,"style":793},[770],[575,2700,2702,2705],{"className":2701},[618],[575,2703,2412],{"className":2704},[618,619],[575,2706,2708],{"className":2707},[721],[575,2709,2711],{"className":2710},[725],[575,2712,2714],{"className":2713},[729],[575,2715,2717],{"className":2716,"style":2565},[733],[575,2718,2719,2722],{"style":2568},[575,2720],{"className":2721,"style":742},[741],[575,2723,2725],{"className":2724},[746,747,748,749],[575,2726,2728,2731],{"className":2727},[618,749],[575,2729,687],{"className":2730},[618,749],[575,2732,1003],{"className":2733},[618,749],[575,2735,2736,2739],{"style":1083},[575,2737],{"className":2738,"style":1071},[741],[575,2740],{"className":2741,"style":1091},[1090],[575,2743,2744,2747],{"style":2609},[575,2745],{"className":2746,"style":1071},[741],[575,2748,2750],{"className":2749},[618],[575,2751,2027],{"className":2752},[618],[575,2754,1111],{"className":2755},[1110],[575,2757,2759],{"className":2758},[729],[575,2760,2762],{"className":2761,"style":2628},[733],[575,2763],{},[575,2765],{"className":2766},[766,1050],[575,2768],{"className":2769,"style":771},[770],[575,2771,2451],{"className":2772},[775],[575,2774],{"className":2775,"style":771},[770],[575,2777,2779,2782],{"className":2778},[609],[575,2780],{"className":2781,"style":2008},[613],[575,2783,2454],{"className":2784},[618],[564,2786,2787,2788,2817],{},"Am stärksten wächst die Population, wenn ",[575,2789,2791,2805],{"className":2790},[578],[575,2792,2794],{"className":2793},[582],[584,2795,2796],{"xmlns":586},[588,2797,2798,2803],{},[591,2799,2800],{},[1001,2801,2802],{},"500",[598,2804,2802],{"encoding":600},[575,2806,2808],{"className":2807,"ariaHidden":605},[604],[575,2809,2811,2814],{"className":2810},[609],[575,2812],{"className":2813,"style":2008},[613],[575,2815,2802],{"className":2816},[618]," Tiere erreicht sind:",[575,2819,2821],{"className":2820},[625],[575,2822,2824,2864],{"className":2823},[578],[575,2825,2827],{"className":2826},[582],[584,2828,2829],{"xmlns":586,"display":634},[588,2830,2831,2861],{},[591,2832,2833,2839,2841,2853,2855,2858],{},[1138,2834,2835,2837],{},[594,2836,657],{},[594,2838,1144],{},[646,2840,663],{},[996,2842,2843,2851],{},[591,2844,2845,2847,2849],{},[594,2846,1153],{},[646,2848,1156],{},[1001,2850,2210],{},[1001,2852,2128],{},[646,2854,2451],{},[1001,2856,2857],{},"7,4",[1662,2859,2860],{}," Jahre",[598,2862,2863],{"encoding":600},"t_W = \\frac{\\ln 19}{0{,}4} \\approx 7{,}4 \\text{ Jahre}",[575,2865,2867,2922,3017],{"className":2866,"ariaHidden":605},[604],[575,2868,2870,2873,2913,2916,2919],{"className":2869},[609],[575,2871],{"className":2872,"style":1201},[613],[575,2874,2876,2879],{"className":2875},[618],[575,2877,657],{"className":2878},[618,619],[575,2880,2882],{"className":2881},[721],[575,2883,2885,2905],{"className":2884},[725,1057],[575,2886,2888,2902],{"className":2887},[729],[575,2889,2891],{"className":2890,"style":1220},[733],[575,2892,2893,2896],{"style":1223},[575,2894],{"className":2895,"style":742},[741],[575,2897,2899],{"className":2898},[746,747,748,749],[575,2900,1144],{"className":2901,"style":1233},[618,619,749],[575,2903,1111],{"className":2904},[1110],[575,2906,2908],{"className":2907},[729],[575,2909,2911],{"className":2910,"style":1243},[733],[575,2912],{},[575,2914],{"className":2915,"style":771},[770],[575,2917,663],{"className":2918},[775],[575,2920],{"className":2921,"style":771},[770],[575,2923,2925,2929,3008,3011,3014],{"className":2924},[609],[575,2926],{"className":2927,"style":2928},[613],"height:2.2519em;vertical-align:-0.8804em;",[575,2930,2932,2935,3005],{"className":2931},[618],[575,2933],{"className":2934},[759,1050],[575,2936,2938],{"className":2937},[996],[575,2939,2941,2996],{"className":2940},[725,1057],[575,2942,2944,2993],{"className":2943},[729],[575,2945,2948,2968,2976],{"className":2946,"style":2947},[733],"height:1.3714em;",[575,2949,2950,2953],{"style":2516},[575,2951],{"className":2952,"style":1071},[741],[575,2954,2956,2959,2965],{"className":2955},[618],[575,2957,1173],{"className":2958},[618],[575,2960,2962],{"className":2961},[618],[575,2963,2103],{"className":2964},[2102],[575,2966,2174],{"className":2967},[618],[575,2969,2970,2973],{"style":1083},[575,2971],{"className":2972,"style":1071},[741],[575,2974],{"className":2975,"style":1091},[1090],[575,2977,2978,2981],{"style":2609},[575,2979],{"className":2980,"style":1071},[741],[575,2982,2984,2987,2990],{"className":2983},[618],[575,2985,1153],{"className":2986},[1321],[575,2988],{"className":2989,"style":1836},[770],[575,2991,2210],{"className":2992},[618],[575,2994,1111],{"className":2995},[1110],[575,2997,2999],{"className":2998},[729],[575,3000,3003],{"className":3001,"style":3002},[733],"height:0.8804em;",[575,3004],{},[575,3006],{"className":3007},[766,1050],[575,3009],{"className":3010,"style":771},[770],[575,3012,2451],{"className":3013},[775],[575,3015],{"className":3016,"style":771},[770],[575,3018,3020,3024,3028,3034,3037],{"className":3019},[609],[575,3021],{"className":3022,"style":3023},[613],"height:0.8889em;vertical-align:-0.1944em;",[575,3025,3027],{"className":3026},[618],"7",[575,3029,3031],{"className":3030},[618],[575,3032,2103],{"className":3033},[2102],[575,3035,2174],{"className":3036},[618],[575,3038,3041],{"className":3039},[618,3040],"text",[575,3042,2860],{"className":3043},[618],[559,3045,3047],{"id":3046},"typische-fehler","Typische Fehler",[886,3049,3050,3265,3367],{},[889,3051,3052,3053,3081,3082,3115,3116,3206,3207,3235,3236,3264],{},"Im Exponenten ",[575,3054,3056,3069],{"className":3055},[578],[575,3057,3059],{"className":3058},[582],[584,3060,3061],{"xmlns":586},[588,3062,3063,3067],{},[591,3064,3065],{},[594,3066,666],{},[598,3068,666],{"encoding":600},[575,3070,3072],{"className":3071,"ariaHidden":605},[604],[575,3073,3075,3078],{"className":3074},[609],[575,3076],{"className":3077,"style":785},[613],[575,3079,666],{"className":3080,"style":789},[618,619]," statt ",[575,3083,3085,3100],{"className":3084},[578],[575,3086,3088],{"className":3087},[582],[584,3089,3090],{"xmlns":586},[588,3091,3092,3098],{},[591,3093,3094,3096],{},[594,3095,666],{},[594,3097,596],{},[598,3099,1958],{"encoding":600},[575,3101,3103],{"className":3102,"ariaHidden":605},[604],[575,3104,3106,3109,3112],{"className":3105},[609],[575,3107],{"className":3108,"style":785},[613],[575,3110,666],{"className":3111,"style":789},[618,619],[575,3113,596],{"className":3114,"style":620},[618,619]," verwenden: Mit ",[575,3117,3119,3145],{"className":3118},[578],[575,3120,3122],{"className":3121},[582],[584,3123,3124],{"xmlns":586},[588,3125,3126,3142],{},[591,3127,3128],{},[640,3129,3130,3132],{},[594,3131,2412],{},[591,3133,3134,3136,3138,3140],{},[646,3135,687],{},[1001,3137,2061],{},[646,3139,669],{},[1001,3141,2352],{},[598,3143,3144],{"encoding":600},"e^{-0{,}0004 \\cdot 5}",[575,3146,3148],{"className":3147,"ariaHidden":605},[604],[575,3149,3151,3155],{"className":3150},[609],[575,3152],{"className":3153,"style":3154},[613],"height:0.8141em;",[575,3156,3158,3161],{"className":3157},[618],[575,3159,2412],{"className":3160},[618,619],[575,3162,3164],{"className":3163},[721],[575,3165,3167],{"className":3166},[725],[575,3168,3170],{"className":3169},[729],[575,3171,3173],{"className":3172,"style":3154},[733],[575,3174,3176,3179],{"style":3175},"top:-3.063em;margin-right:0.05em;",[575,3177],{"className":3178,"style":742},[741],[575,3180,3182],{"className":3181},[746,747,748,749],[575,3183,3185,3188,3191,3197,3200,3203],{"className":3184},[618,749],[575,3186,687],{"className":3187},[618,749],[575,3189,1173],{"className":3190},[618,749],[575,3192,3194],{"className":3193},[618,749],[575,3195,2103],{"className":3196},[2102,749],[575,3198,2107],{"className":3199},[618,749],[575,3201,669],{"className":3202},[797,749],[575,3204,2352],{"className":3205},[618,749]," kämen nach ",[575,3208,3210,3223],{"className":3209},[578],[575,3211,3213],{"className":3212},[582],[584,3214,3215],{"xmlns":586},[588,3216,3217,3221],{},[591,3218,3219],{},[1001,3220,2352],{},[598,3222,2352],{"encoding":600},[575,3224,3226],{"className":3225,"ariaHidden":605},[604],[575,3227,3229,3232],{"className":3228},[609],[575,3230],{"className":3231,"style":2008},[613],[575,3233,2352],{"className":3234},[618]," Jahren ungefähr ",[575,3237,3239,3252],{"className":3238},[578],[575,3240,3242],{"className":3241},[582],[584,3243,3244],{"xmlns":586},[588,3245,3246,3250],{},[591,3247,3248],{},[1001,3249,1996],{},[598,3251,1996],{"encoding":600},[575,3253,3255],{"className":3254,"ariaHidden":605},[604],[575,3256,3258,3261],{"className":3257},[609],[575,3259],{"className":3260,"style":2008},[613],[575,3262,1996],{"className":3263},[618]," Tiere heraus, also praktisch keine Änderung.",[889,3266,3267,3268,3366],{},"Glauben, das Wachstum sei am Anfang am größten: Das gilt beim beschränkten Wachstum. Beim logistischen Wachstum ist die Zunahme bei ",[575,3269,3271,3289],{"className":3270},[578],[575,3272,3274],{"className":3273},[582],[584,3275,3276],{"xmlns":586},[588,3277,3278,3286],{},[591,3279,3280],{},[996,3281,3282,3284],{},[594,3283,596],{},[1001,3285,1003],{},[598,3287,3288],{"encoding":600},"\\frac{S}{2}",[575,3290,3292],{"className":3291,"ariaHidden":605},[604],[575,3293,3295,3298],{"className":3294},[609],[575,3296],{"className":3297,"style":1043},[613],[575,3299,3301,3304,3363],{"className":3300},[618],[575,3302],{"className":3303},[759,1050],[575,3305,3307],{"className":3306},[996],[575,3308,3310,3355],{"className":3309},[725,1057],[575,3311,3313,3352],{"className":3312},[729],[575,3314,3316,3330,3338],{"className":3315,"style":1064},[733],[575,3317,3318,3321],{"style":1067},[575,3319],{"className":3320,"style":1071},[741],[575,3322,3324],{"className":3323},[746,747,748,749],[575,3325,3327],{"className":3326},[618,749],[575,3328,1003],{"className":3329},[618,749],[575,3331,3332,3335],{"style":1083},[575,3333],{"className":3334,"style":1071},[741],[575,3336],{"className":3337,"style":1091},[1090],[575,3339,3340,3343],{"style":1094},[575,3341],{"className":3342,"style":1071},[741],[575,3344,3346],{"className":3345},[746,747,748,749],[575,3347,3349],{"className":3348},[618,749],[575,3350,596],{"className":3351,"style":620},[618,619,749],[575,3353,1111],{"className":3354},[1110],[575,3356,3358],{"className":3357},[729],[575,3359,3361],{"className":3360,"style":1118},[733],[575,3362],{},[575,3364],{"className":3365},[766,1050]," am größten.",[889,3368,3369,3370,3413,3414,1453],{},"Annehmen, die Schranke werde nach endlicher Zeit erreicht: ",[575,3371,3373,3392],{"className":3372},[578],[575,3374,3376],{"className":3375},[582],[584,3377,3378],{"xmlns":586},[588,3379,3380,3390],{},[591,3381,3382,3384,3386,3388],{},[594,3383,644],{},[646,3385,654],{"stretchy":653},[594,3387,657],{},[646,3389,660],{"stretchy":653},[598,3391,914],{"encoding":600},[575,3393,3395],{"className":3394,"ariaHidden":605},[604],[575,3396,3398,3401,3404,3407,3410],{"className":3397},[609],[575,3399],{"className":3400,"style":807},[613],[575,3402,644],{"className":3403,"style":717},[618,619],[575,3405,654],{"className":3406},[759],[575,3408,657],{"className":3409},[618,619],[575,3411,660],{"className":3412},[766]," bleibt immer kleiner als 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