Suppose that the logistic equation dx/dt = kx(M − x) models a population x(t) of fish in a...

Suppose that the logistic equation dx/dt = kx(M − x) models a population x(t) of fish in a lake after t months during which no fishing occurs. Now suppose that, because of fishing, fish are removed from the lake at the rate of lix fish per month (with h a positive constant). Thus fish are “harvested” at a rate proportional to the existing fish population, rather than at the constant rate of Example. (a) II 0 > h < kM, show that the population is Still logistic. What is the new limiting population? If

show that

so the lake is eventually fished out.