A model that describes the population of a fishery in which harvesting takes place at a constant rate is given by dP dt = kP - h, where k and h are positive constants. (a) Solve the DE subject to P (0) = P0. P (t) = (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 P (t) decreases as t increases P (t) increases as t increases P (t) = 0 for every t P (t) = P0 for every t P0 = h/k P (t) decreases as t increases P (t) increases as t increases P (t) = 0 for every t P (t) = P0 for every t 0 < P0 0 such that P (T) = 0. If the population goes extinct, then find T. (If the population does not go extinct, enter DNE.)

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Patrick Stout

5 May, 17:55

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Dawson · Answer 1

It increases at T because the behavior increased its speed