## Calculus: Early Transcendentals 8th Edition

a) $P_{n}=1.08P_{n-1}-300$ b) After six months, the number of catfish in the pond is 5734.
a) $P_{0}=5000$ Each month the number of catfish increases by 8% and 300 catfish are utilized. So after (n-1) months, the number of catfish is $P_{n-1}$. $P_{n}=(P_{n-1}+\frac{(P_{n-1}) \times 8}{100})-300$ $P_{n}=1.08P_{n-1}-300$ b) $P_{0}=5000$ $P_{1}=1.08P_{0}-300=5100$ $P_{2}=1.08P_{1}-300=5208$ $P_{3}=1.08P_{2}-300=51324.64$ $P_{4}=1.08P_{3}-300=5450.61$ $P_{5}=1.08P_{4}-300=5586.66$ $P_{6}=1.08P_{5}-300=5733.59$ After six months, the number of catfish in the pond is 5734.