Constant-Harvest Model A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by
where k and h are positive constants.
(a) Solve the DE subject to P(0) = P0.
(b) Describe the behavior of the population P(t) for increasing time in the three cases P0>h/k, P0=h/k, and 0 < P0<h/k.
(c) Use the results from part (b) to determine whether the fish population will ever go extinct in finite time, that is, whether there exists a time T > 0 such that P(T) = 0. If the population goes extinct, then find T.
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