Question

A pond on a fish farm has a carrying capacity of 1000 fish. The pond was originally stocked

with 100 fish. Let N(t) denote the number of fish in the pond after t months.

a) Set up a logistic differential equation satisfied by N(t), and plot an approximate graph

of a fish population.

b) Find the size of the population of fish with the highest rate of growth. Find this rate

given that the intrinsic rate of growth is 3.