In a certain environment live 10000 particularly harmful insects of species X .

Question

In a certain environment live 10000 particularly harmful insects of species X. In the hope of eradicating species X, 1000 insects of species Y, which eat species X, are introduced. Let X(t) be the number of thousands of insects of species X, and Y(t) be the number of thousands of insects of species Y, at time t (in years) after species Y is introduced. Suppose the sizes of the populations are governed by

x'=5x-y ,y'=5x+y

  A/     Both species survive indefinitely

  B/     Both species survive for approximately 2.7 years, at which time species X

is eradicated.

  C/     Both species survive for approximately 3.2 years, at which time species Y

dies ouT

Explanation / Answer

C/ Both species survive for approximately 3.2 years, at which time species Y

dies ouT

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