Get answer: Use a graphing utility to graph the functions and when Describe the behavior

Chapter 6, Problem 24

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In Exercises 23 and 24, consider a competing species relationship involving bass and trout. Assume the bass and trout compete for the same resources. Let x represent the number of bass (in thousands), let y represent the number of trout (in thousands), and let t represent the time in months. Assume that the following competing-species equations model the rates of change of the two populations.

\(\frac{d x}{d t}=0.8 x-0.4 x^{2}-0.1 x y\)                       Rate of change of bass population

\(\frac{d y}{d t}=0.3 y-0.6 y^{2}-0.1 x y\)                       Rate of change of trout population

When t = 0, x = 9 and y = 5.

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

Text Transcription:

frac d x d t=0.8 x-0.4 x^2-0.1 x y

frac d y d t=0.3 y-0.6 y^{2}-0.1 x y

0 leq t leq 36