A fish farmer has 5000 catfish in a pond. The number of catfish increases by 8% per month and the farmer harvests 420 catfish per month.

a). Find a recursive equation for the catfish population Pn for each month.

b). Solve the recursive equation to find an explicit equation for the catfish population.

c). How many catfish are in the pond after six months?

d). Is harvesting 420 catfish per month a sustainable strategy for the fish farmer?

e). What is the maximum number of catfish the fish farmer can harvest to sustain his business?