Biologists stocked a lake with 800 fish and estimated the carrying capacity of the lake to be 20000. In the first year, the number of fish doubled. Use a logistic model to model the fish population and answer the questions below.

A) Find an expression for the size of the fish population P=P(t) at time t years. (You may approximate the constant k to six decimal places)

B) How long will it take for the fish population to reach 10000? (Approximate to three decimal places)

Question

Biologists stocked a lake with 800 fish and estimated the carrying capacity of the lake to be 20000. In the first year, the number of fish doubled. Use a logistic model to model the fish population and answer the questions below.

A) Find an expression for the size of the fish population P=P(t) at time t years. (You may approximate the constant k to six decimal places)

B) How long will it take for the fish population to reach 10000? (Approximate to three decimal places)

anonymous · Answer

Would I use the equation $$P=M/(1+Ae^-kt)$$ where M is the carrying capacity.

anonymous · Answer

P=20000/[1+24e^(-.735707t)]?