Question: differential equations question help 2. [APPM 2360 (10 pts)] The population, P. of fish in a lake grows logistically and is harvested at a constant

differential equations question help

2. [APPM 2360 (10 pts)] The population, P. of fish in a lake grows logistically and is harvested at a constant rate. The differential equation describing the population is dP dt = P(8 - P) - 12 where t is in years and P is in hundreds of fish. Use the direction field below to answer the following questions. (a) (3 pts) For what initial populations will the fish go extinct in a finite number of years? (b) (7 pts) Are there any initial fish populations that will sustain themselves after a long time? If so, find them and determine the number of fish that will exist in these situations. If not, explain why not

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