Replacement time. An office copier has an initial price of $2,500. A service contract cost...

Replacement time. 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

(A) Find the rational function

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(B) Sketch a graph of

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(C) When is the average cost per year at a minimum, and what is the minimum average annual cost? [Hint: Refer to the sketch in part (B) and evaluate (n) at appropriate integer values until a minimum value is found.] The time when the average cost is minimum is frequently referred to as the replacement time for the piece of equipment.

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