In a fish farm, a population of fish is introduced into a pond and is harvested regularly. A model for the rate of change of the fish population is given by the equation $\displaystyle \frac{dP}{dt}= r_0 (1-\frac{P(t)}{P_c})P(t)-\beta P(t)$, where $r_0$ is the birth rate of the fish, $P_c$ is the maximum population that the pond can sustain, and $\beta$ is the percentage of the population that can be harvested.

(a) What value of $dP/dt$ corresponds to a stable population?
(b) If the pond can sustain 10,000 fish, the birth rate is 5 percent and the harvesting rare is 4 percent, find the stable population level.

(a)
(b)