A car with an initial cost of $26,500 depreciates at a rate of 7.5% per year. Write the function that models this situation. Then use your formula to determine when the value of the car will be $15,000 to the nearest year.

Question

Mathematics

Esteban Wade

17 May, 06:12

A car with an initial cost of $26,500 depreciates at a rate of 7.5% per year. Write the function that models this situation. Then use your formula to determine when the value of the car will be $15,000 to the nearest year.

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Answers (1)

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Gabby · Answer 1

f (x) = 26500 * (0.925) ^x

It will take 7 years

Step-by-step explanation:

A car with an initial cost of $26,500 depreciates at a rate of 7.5% per year. Write the function that models this situation. Then use your formula to determine when the value of the car will be $15,000 to the nearest year.

To find the formula we will use this formula: f (x) = a * b^x. A is our initial value which in this case is $26500. B is how much the value is increasing or decreasing. In this case it is decreasing by 7.5% per year. Since the car value is decreasing we will subtract 0.075 from 1. This will result in the formula being f (x) = 26500 * (0.925) ^x. Now to find the value of the car to the nearest year of when the car will be 15000 we plug 15000 into f (x). 15000 = 26500 * (0.925) ^x. First we divide both side by 26500 which will make the equation: 0.56603773584 = (0.925) ^x. Then we will root 0.56603773584 by 0.925. This will result in x being 7.29968 which is approximately 7 years.