Chapter 6.6, Problem 13E

Prairie Dogs and Black-Footed Ferrets In Exercises 15-16, consider a predator-prey relationship involving black-footed ferrets (predators) and prairie dogs (prey). Let xrepresent the number of prairie dogs, let yrepresent the number of black-footed ferrets, and let trepresent the time in months. Assume that the following predator-prey equations model the rates of change of each population.

$\begin{array}{ll}\frac{dx}{dt}=0.1x-0.00008xy\hfill & \text{Rate of change of prey population}\hfill \\ \frac{dy}{dt}=-0.4y+0.00004xy\hfill & \text{Rate of change of predator population}\hfill \end{array}$

When $t=0,x=4000$ and $y=1000$.

Find the critical points of the predator-prey equations.