Question

An outboard motor has an initial price of $1,470. A service contract costs $200 for the first year and increases $120 per year thereafter. The total cost of the outboard motor (in dollars) after n years is given by C(n)=1,470 + 150n + 301², where n21. Complete parts (A) through (C). (A) Write an expression for the average cost per year, Čín), for n years. Č(n) = (B) Graph the average cost function found in part (A). Choose the correct graph below. ОА. Ов. Ос. OD Ay 4,500 4,500 Q 4,500 4,500 tu (C) When is the average cost per year minimum? (This time is frequently referred to as the replacement time for this place of equipment.) The average cost per year is minimum after years. your

Answer 1

The initial price of the outboard motor is $1,470. The total cost of the outboard motor (in dollars) after years is C(x) = 1,470+150n+30n", where n 21. The average cost function is C(x)=C(n) 72 1,470 +150n +30n2 =C(n)= 72 1,470 =C(x) = +150+30n, where n21 The graph of the average cost function found in part (A) 1,470 (n) = +150+30n is shown below.

4500 20

The correct graph is (A). (C) C*(n) = d (1,470 hamile +150+30n 72 1,470 +0+30 30n2 - 1,470 2 For the minimum average cost: C'(x) = 0 3012 -1,470 0 = 2 2 = 30n2 - 1,470 = 0 => 30n2 = 1,470 1,470 30 =n2 = 49 n=7 Thus, the average cost per year is minimum after years