Use the predator-prey equations and the slope field in Exercise 11 to graph the solution

Chapter 6, Problem 12

(choose chapter or problem)

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

\(\frac{d x}{d t}=0.8 x-0.04 x y\)                           Rate of change of prey population

\(\frac{d y}{d t}=-0.3 y+0.006 x y\)                      Rate of change of predator population

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

Use the predator-prey equations and the slope field in Exercise 11 to graph the solution curve using the initial conditions. Describe the changes in the rabbit and fox populations as you trace the solution curve.

Text Transcription:

frac d x d t=0.8 x-0.04 x y

frac d y d t=-0.3 y+0.006 x y