Question

Amber bought a used car valued at  16,000. When this car was new, it was sold for16,000.Whenthiscarwasnew,itwassoldfor 28,000. If the car depreciates exponentially at a rate of 9% per year, approximately how old is the car?​

Answer 1

The car is about a year old if it depreciates exponentially at a rate of 9% per year

In order to know how old the car is, we will use the depreciation formula expressed below:

$P_t=P_0e^{rt$

Pt is the final price = 16000

P0  is the initial price = 28000

Given the rate of 0.09

Substitute the given parameters into the formula to get the time "t"

$16000=28000e^{-0.09t}\\\frac{16000}{28000}=e^{-0.09t}\\ 0.5714=0.9139t\\t =\frac{0.5714}{0.9139} \\t=0.62$

This shows that the car is about a year old if it depreciates exponentially at a rate of 9% per year

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