Question 1066955: The yearly depreciation rate for a car is modeled by r=1-(V/C)^1/8 , where V is the value of the car after n years and C is the orignal cost.
a. Determine the depreciation rate for a car the originally cost $14,000 and is worth $10,000 after 5 years, Round to the nearest tenth of a percent.
b. Determine the original cost of a car that has a yearly depreciation rate of 18% and is worth $14,000 after 3 years. Round to the nearest $100.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The yearly depreciation rate for a car is modeled by r=1-(V/C)^1/8 , where V is the value of the car after n years and C is the orignal cost.
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a. Determine the depreciation rate for a car the originally cost $14,000 and is worth $10,000 after 5 years, Round to the nearest tenth of a percent.
r = 1-(10,000/14000)^(1/8) = 1-(5/7)^(1/8) = 0.041 = 4.1%
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b. Determine the original cost of a car that has a yearly depreciation rate of 18% and is worth $14,000 after 3 years. Round to the nearest $100.
0.18 = 1-(14000/C)^(1/8)
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0.82 = (14000/C)^(1/8)
0.204 = 14000/C
C = 14000/0.204
Original cost = $68,488.43
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Cheers,
Stan H.
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