Solved: Fish harvesting A fishery manager knows that her

Solution:-

Step1

Given that

Let Fn be the fish population after the nth month, where F0 = 4000 fish.

A fishery manager knows that her fish population naturally increases at a rate of 1.5% per month. At the end of each month, 120 fish are harvested.

Step2

To find

Assuming that this process continues indefinitely, what is the long-term (steady-state) population of the fish?

Step3

 Suppose the natural growth rate is r (1.5%), that a(= 120) fish are taken out each month, and that the initial population is F0(= 4000).

Then the population develops according to the recursive relation Fn+1 = (1 + r)Fn − a

where the first expression reflects the natural growth, and the second expression is due to fish harvesting.

By writing the first terms we can see how a pattern develops

 = (1 + r) − a