Investigate the following harvesting model both qualitatively and analytically. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population P(t) of the fishery at time t is given by: dP /dt = P(a − bP) − h, P(0) = P0, where a, b, h, and P0 are positive constants.

Suppose a = 9, b = 1, and h = 81/4.

Required:
Determine whether the population becomes extinct in finite time.

a. The population becomes extinct in finite time if P0 > 9 2 .
b. The population becomes extinct in finite time if P0 = 9 2 .
c. The population becomes extinct in finite time for all values of P0.
d. The population becomes extinct in finite time if P0 < 9 2 .