#### Problem 67E

67. A fish farmer has 5000 catfish in his pond. The number of catfish increases by $8 \%$ per month and the farmer harvests 300 catfish per month.

(a) Show that the catfish population $P_{n}$ after $n$ months is given recursively by

$$P_{n}-1.08 P_{n-1}-300 \quad P_{0}-5000$$

(b) How many catfish are in the pond after six months?