Chapter 25, Problem 21P

The logistic model is used to simulate population as in

$\frac{dp}{dt}=k_{gm}\left(1-p/p_{\text{max}}\right)p$

where $p=$ population, $k_{gm}=$ the maximum growth rate under unlimited conditions, and $p_{\text{max}}=$ the carrying capacity. Simulate the world's population from 1950 to 2000 using one of the numerical methods described in this chapter. Employ the following initial conditions and parameter values for your simulation: $p_0\left(\text{in 1950}\right)=2555\text{ million people, }{k}_{gm}=0.026/\text{yr, and }{p}_{\text{max}}=12,00$ million people. Have the function generate output corresponding to the dates for the following measured population data. Develop a plot of your simulation along with these data.

t	1950	1960	1970	1980	1990	2000
p	2555	3040	3708	4454	5276	6079