A farmer buys a new tractor for $158,000 and assumes that it will have a trade-i

Question

A farmer buys a new tractor for $158,000 and assumes that it will have a trade-in value of $82,000 after 10 years. The farmer uses a constant rate of depreciation to determine the annual value of the tractor. (A) Find a linear model for the depreciated value V of the tractor t years after it was purchased. V = (Type your answer in slope-intercept form.) (B) What is the depreciated value of the tractor after 6 years? The depreciated value of the tractor after 6 years is $. (C) When will the depreciated value fall below $40,000? The depreciated value will fall below $40,000 during the th year. (D) Graph V for 0 lessthanorequalto t lessthanorequalto 20. Choose the correct graph below.

Explanation / Answer

(A) Value V(0) when t = 0 is $158000

Value V(10) when t = 10 is $82000

=> Slope = (V(10)-V(0)) / (10-0)

= (82000 - 158000) / 10

= -7600

Thus V = -7600t + c

When t = 0, V(0) = 158000

=> 158000 = -7600*0 + c

=> c = 158000

=> V = -7600t + 158000

(B) When t = 6

V(6) = -7600*6 + 158000

=> V(6) = -45600 + 158000

=> V(6) = $112400

(C) When V(t) = 40000

=> 40000 = -7600t + 158000

=> 7600t = 158000 - 40000

=>7600t = 118000

=> t = 118000/7600

=> t = 15.53 or during the 16th year.

(D) When t = 0, V(0) = $158000

When t = 20, V(20) = -7600*20 + 158000 = $6000

Note that the slope is decreasing and 158000 is closer to 170000. So the correct answer is c.

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