A car that originally cost $20,000 depreciates by 15% each year. In about how many years will the car be worth half its value? Use the equation 10,000 = 20,000 (8.5) ^x to solve the problem. Round your answer to the nearest dollar.

Question

Summer Park

Mathematics

16 October, 00:05

A car that originally cost $20,000 depreciates by 15% each year. In about how many years will the car be worth half its value? Use the equation 10,000 = 20,000 (8.5) ^x to solve the problem. Round your answer to the nearest dollar.

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Answers (1)

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Cason Solomon · Answer 1

It's

0.5=0.85^x take natural log of both sides ...

ln0.5 / (ln0.85) = x

x≈4.265 years the car's value will be half of its original value ...

y=20000 (0.85) ^ (4.265)

y=$10000.00