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 = 7, b = 1, and h = 49 4 .

Determine whether the population becomes extinct in finite time.

a. The population does not become extinct in finite time.
b. The population becomes extinct in finite time for all values of Po.
c. The population becomes extinct in finite time if Po > 7/2
d. The population becomes extinct in finite time if Po < 7/2
e. The population becomes extinct in finite time if Po= 7/2

If so, find that time. (If not, enter NONE.)
t=