PROBLEM 42E

Constant-Harvest Model A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by

where k and h are positive constants.

(a) Solve the DE subject to P(0) = P0.

(b) Describe the behavior of the population P(t) for increasing time in the three cases and

(c) Use the results from part (b) to determine whether the fish population will ever go extinct in finite time, that is, whether there exists a time T > 0 such that P(T) = 0. If the population goes extinct, then find T.

Solution

Step 1

In this problem, we have to solve the differential equation subject to

b) Explain the scenario when , .

c) We have to determine the fist population at finite time.