Chapter 9, Problem 39P

The population growth of species with limited capacity can be modeled by the equation:

$\frac{dN}{dx}=kN\left(1-\frac{N}{N_{\max }}\right)-r\frac{N^2}{N_c}$

where N is the population size, N_maxis the limiting number for the population, and k, r, and N, are constants. The second term in the equation represent the effect of predation. Consider the case where N_max= 6,000, k = 0.196 l/yr, r = 40 1/yr, N = 3,000, and N(0) = 50. Determine N for $0\le t\le 50$ yr. Make a plot of N as a function of t.