A fishery manager knows that her fish population naturally increases at a rate of 1.3% per month, while 83 fish are harvested each month. Let F, be the fish population after the nth month, where F, = 4000 fish. Answer parts a-e below. a. Write out the first five terms of the sequence {Fn}. Fo = 4000 F1 = 3969 F2 = 3938 F3 = 3906 F4 = 3874 (Simplify your answers. Round to the nearest integer as needed.) b. Find a recurrence relation that generates the sequence {Fn}. Fn = 1.013F, 83 c. Does the fish population decrease or increase? The fish population decreases. d. Determine whether the fish population decreases or increases in the long run if the initial population is 5700 fish. The fish population decreases in the long run if the initial population is 5700 fish. e. Determine the initial population Fo below which the population decreases. The initial population Fo below which the population decreases is 6385 fish. (Round up to the nearest whole number.)

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