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A car is purchased for $17,000 and its value decreases every year by 14%. What is the equation for this?

Since the value of the car is reduced by 14% each year , at the end of each year , the value if the car is 86% of the value from the previous year.

At the end of the first year , the value of the car is .86 x 17,000

At the end of the second year , the value of the car is .86 x .86 x 17,000 = .86^2 x 17,000

At the end of the third year , the value of the car is .86 x .86 x .86 x 17,000 = .86^3 x 17,000

The pattern should be clear, if v(n) is the value of the car after n years ,

v(n) = .86^n x 17,000

Algebra

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