A new car begins to decrease in value, or depreciate, from the moment it is purc

Question

A new car begins to decrease in value, or depreciate, from the moment it is purchased. Suppose a new car purchased for exist25.000 in July of 2013 depreciates by 17% each year. When the value reaches exist500, depreciation stops and the car is worth exist500 from then on. In what year will the value of the car reach exist500? Find the rate of depreciation for a car that takes 7 years to lose two-thirds of its value. Give your answer to the nearest tenth of a percent. In 2015, Sarah's truck, which she bought used in 2009 for exist13, 995.36, is worth exist4477.31. Find the price paid by the original owner in 2004 to the nearest thousand dollars.

Explanation / Answer

Intial value , po = $25000

final value , p' = $ 500

P' = Po(1 - 0.17)^t

= Po(0.83)^t

500 = 25000(0.83)^t

1/5 = 0.83^t

take natural log on both sides:

ln(1/5) = t*ln(0.83)

t = ln(1/5)/ln(0.83)

= 8.637

Year 2013 + 8.637 = 2022

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