A fishery manager knows that her fish population naturally increases at a rate of 1.5% per month, while 80 fish are harvested each month. Let F_n be the fish population after the nth month, where F₀ = 4000 fish.

a. Write out the first five terms of the sequence {F_n}.

b. Find a recurrence relation that generates the sequence {F_n}.

c. Does the fish population decrease or increase in the long run?

d. Determine whether the fish population decreases or increases in the long run if the initial population is 5500 fish.

e. Determine the initial fish population F₀ below which the population decreases.