If a pond can support up to 10,000 fish, the rate of growth of the fish population is jointly proportional to the number

of fish present and the difference between 10,000 and the number present. The rate of growth is 210 fish per week when

3000 fish are present.

a. Find a mathematical model expressing the rate of population growth as a function of the number present.

b. What is the domain of the function in part (a)?

c. Compute the size of the fish population for the growth rate to be a maximum. (Note: If possible, simplify your results.

Do not approximate.)