Differential Model Equations

TABLE 3.1 A comparison of the Malthusian and Logistic Models with U.S Census Data (Population is given in Millions) Year U.S. Census Malthusian (Example 3) Logistic (Example 4) Logistic (Least Squares) 1790 3.93 3.93 3.93 4.11 1800 5.31 5.19 5.3 0.0312 5.42 1810 7.24 6.84 7.13 0.0299 7.14 1820 9.64 9.03 9.58 0.0292 9.39 1830 12.87 11.92 12.82 0.0289 12.33 1840 17.07 15.73 17.07 0.0302 16.14 1850 23.19 20.76 22.6 0.031 21.05 1860 31.44 27.4 29.7 0.0265 27.33 1870 39.82 36.16 38.66 0.0235 35.28 1880 50.19 47.72 49.71 0.0231 45.21 1890 62.98 62.98 62.98 0.0207 57.41 1900 76.21 83.12 78.42 0.0192 72.11 1910 92.23 109.69 95.73 0.0162 89.37 1920 106.02 144.76 114.34 0.0146 109.1 1930 123.2 191.05 133.48 0.0106 130.92 1940 132.16 252.13 152.26 0.0106 154.2 1950 151.33 333.74 169.9 0.0156 178.12 1960 179.32 439.12 185.76 0.0145 201.75 1970 203.3 579.52 199.5 0.0116 224.21 1980 226.54 764.8 211 0.01 244.79 1990 248.71 1009.33 220.38 0.011 263.01 2000 281.42 1332.03 227.84 0.0107 278.68 2010 308.72 1757.91 233.68 291.8 2020 ? 2319.95 238.17 302.56