Problem 4E

Modify the model in Problem 3 for net rate at which the population P(t) of a certain kind of fish changes by also assuming that the fish are harvested at a constant rate h > 0.

Reference : problem 3

Using the concept of net rate introduced in Problem 2, determine a model for a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t.

Solution :

Step 1 :

In this problem we have to determine the model for population.

We know that “the new population model is the difference between the rate of birth and the rate of death”.