A vector y = [R(t) F(t)]T describes the populations of some rabbits R(t) and foxes F(t). The...

A vector y = [R(t) F(t)]^T describes the populations of some rabbits R(t) and foxes F(t). The populations obey the system of differential equations given by y′ = Ay where

A =

146	−1656
12	−136

The rabbit population begins at 84000. If we want the rabbit population to grow as a simple exponential of the form R(t) = R₀e^8t with no other terms, how many foxes are needed at time t = 0?
(Note that the eigenvalues of A are λ = 8 and 2.)

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Expert Solution

Colby Messinger answered 11 hours ago

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