Question

4. Suppose that the logistic equation dt Pla -bP) models a population of fish in a lake after t months during which no fishing occurs. What is the limiting population for this fish population? suppose that, because of fishing, fish are removed from the lake at a rate proportional to the existing fish population. i. Write a differential equation that describes this situation. ii. Show that if the constant of proportionality for the harvest of fish, h, is between 0 and a, the population is still logistic. What is the new limiting population in this case? a. ili. Ifh 2 a, show that P(t) 0 ast, so that the lake is eventually fished out

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