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Chapter 7: Q67E (page 325)

Consider the coyotes鈥搑oadrunner system discussed in Example 7. Find closed formulas for c(t) and r(t), for the initial populations c0= 100, r0 = 800.

Short Answer

Expert verified

The solutions are, c(t)=300(1.1)t-200(0.9)t

r(t)=900(1.1)t-100(0.9)t

Step by step solution

01

Solving for eigenvalues

The eigenvalues of the system are 位1=1,1 and a00

位2=0.9

The corresponding eigenvectors are

v1鈫�=100300

And

v2鈫�=200100

02

Solving further

So far,

x0鈫�=3v鈫�1+v2鈫�

Therefore, by theorem 7.1.3, we have

x鈫�t=3(1.1t100300-0.9t200100

The solutions are,c(t)=300(1.1)t-200(0.9)tr(t)=900(1.1)t-100(0.9)t

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Most popular questions from this chapter

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

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For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

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