2 / 3 - 100% -+ 3. 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(1) at time : in 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)