% 定义时间（年份）和人口数据t = [1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020];p = [3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 38.6 50.2 62.9 76.0 92.0 106.5 123.2 131.7 150.7 179.3 204.0 226.5 251.4 281.4 309.3 329.4];% 将年份转换为连续变量，从1790年开始t = t - 1790;% 定义Logistic模型logisticModel = @(b, x) b(1) ./ (1 + ((b(1)/b(2) - 1) * exp(-b(3) * x)));% 初始参数估计initialParams = [max(p), p(1), 0.02]; % K, P0, r% 使用非线性最小二乘法拟合参数options = optimset('Display', 'off');beta = lsqcurvefit(logisticModel, initialParams, t, p, [], [], options);K = beta(1); % 承载力P0 = beta(2); % 初始人口r = beta(3); % 增长率p_pred = logisticModel(beta, t);figure;plot(t + 1790, p, 'bo', t + 1790, p_pred, 'r-');xlabel('Year');ylabel('Population (millions)');legend('Actual Data', 'Logistic Model');title('Logistic Growth Model for US Population');t_2030 = 2030 - 1790;p_2030 = logisticModel(beta, t_2030);fprintf('Logistic Model预测2030年人口: %.2f million\n', p_2030);