Chapter 6.6, Problem 10E

Rabbits and Foxes In Exercises 9-12, consider a predator-prey relationship involving foxes (predators) and rabbits (prey). Let xrepresent the number of rabbits, let yrepresent the number of foxes, and let trepresent the time in months. Assume that the following predator-prey equations model the rates of change of each population.

$\begin{array}{ll}dx/dt=0.8x-0.04xy\hfill & \text{Rate of change of prey population}\hfill \\ dy/dt=-0.3y+0.006xy\hfill & \text{Rate of change of predator population}\hfill \end{array}$

When $t=0,x=55$ and $y=10$.

10. Use a graphing utility to graph the functions x and y when $0\le t\le 36$. Describe the behavior of each solution as t increases.