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 of fish
present. The rate of growth is 90 fish per week when 1, 000 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 your function in part (a)?

c. What is the size of the fish population for the growth to be a maximum?

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