Suppose that the logistic equation dx=dt D kx.M x/ models
Chapter , Problem 23(choose chapter or problem)
Suppose that the logistic equation dx=dt D 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 hx 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 4. (a) If 0 < h < kM, show that the population is still logistic. What is the new limiting population? (b) If h = kM, show that x.t / ! 0 are t ! C1, so the lake is eventually fished out.
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