PROBLEM 39E

Population Model Another population model is given by

where h and k are positive constants. For what initial values P(0) = P0 does this model predict that the population will go extinct?

Solution:-

Step1

Given that

We have to find that for what initial values P(0) = does this model predict that the population will go extinct?

Step2

We have

Population model

-----------------------(1)

where h and k are positive constants.

The equation is first order linear differential equation.

By using integrating factor

Step3

Solution for equation (1) is given by

=

Where C is integration constant.

From (2) we get

P(t)=

Step4

When P(0)=

Put in (3) we get

If

This shows that is the equilibrium solution.

Step5

This means the population will go extinct,

Therefore, the population becomes extinct when,