Chapter 10, Problem 18P

The Verhulst model, given in the following equation, describes the growth of a population that is limited by various factors such as overcrowding and lack of resources:

$N(t)=\frac{N_{\infty }}{1+\left(\frac{N_{\infty }}{N_0}-1\right)e^{-rt}}$

where N(t) is the number of individuals in the population. N₀is the initial population size, N₈is the maximum population size possible due to the various limiting factors, and r is a rate constant. Make a surface plot of N(t) versus t and N assuming r = 0.1 s-l, and N₀= 10. Let t vary between 0 and 100 and N₈between 100 and 1,000.