Suppose that the logistic equation dx dt = kx(mx) models a population x(t) of discus fish in a lake after t months during which no fishing occurs. let us now suppose that discus fish are removed from the lake to sell it as an ornamental pet, and the rate of removal is hx fish per month (h > 0). we thus observe that fish are harvested at a rate proportional to the existing fish population, rather than at a constant rate of example.
ii 0> h 0 are t -> +∞ so the lake is eventually fished out.