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.
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