Answer
a)
$P_{n}=1.08P_{n-1}-300$
b)
After six months, the number of catfish in the pond is 5734.
Work Step by Step
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.
