An office copier has an initial price of $2,500. A service contract costs $200 for the first year and increases $50 per year thereafter. It can be shown that the total cost of the copier after n years is given by

C(n) = 2,500 + 175n + 25n²

The average cost per year for n years is given by

C̅(n) = C(n) / n.

(A) Find the rational function C̅.

(B) Sketch a graph of C̅ for 2 ≤ n ≤ 20.

(C) When is the average cost per year at a minimum, and what is the minimum average annual cost? The time when the average cost is minimum is frequently referred to as the replacement time for the piece of equipment.

(D) Graph the average cost function C̅ on a graphing calculator and use an appropriate command to find when the average annual cost is at a minimum.