Mathematics

Logan Ray

25 March, 12:39

Biology A lake is stocked with 500 fish, and the fish population p begins to increase according to the logistic growth model

p = 10,000/1 + 19e-t/5, t > 0

where t is measured in months.

(a) Find the number of fish in the lake after 4 months.

(b) Use a graphing utility to graph the model. Find the number of months it takes for the population of fish to reach 4000.

(c) Does the population have a limit as t increases without bound? Explain your reasoning.