A new car is purchased for 17000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 12 years?
The first year the $17000 car depreciates by 13.5% so by 0.135(17000) to $17000- 0.135(17000)= $17000(1- 0.135)= $17000(0.865). The next year it depreciates to ($17000(0.865))(0.865)= $17000(0.865^2). Every year the same thing happens- the value is multiplied by 0.865 so the value after 12 years is $17000(0.865^12)= $2982.92.
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