Fish in a lake grow logistically toward a carrying capacity of fish

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Fish in a lake grow logistically toward a carrying capacity of

10\,000

fish. The proportionality constant is

0.5\,(\text{fish})^{-1}\,\text{month}^{-1}

when the population is below

5\,000

fish and

0.3\,(\text{fish})^{-1}\,\text{month}^{-1}

when the population is

5\,000

fish or more. Compare the instantaneous growth rates when the population is

4\,000

fish versus

6\,000

fish and indicate which size experiences the faster growth.