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Alex purchased a new car for $28,000. The car's value depreciates 7.25% each year. What will be the value of the car 5 years after it is purchased? Round your answer to the nearest dollar.

Verified Answer :

W0lf93

First Year - $28,000 with a 7.25% depreciation = 28000 * 7.25% = 2,030 - 28000 = $25,970

Second Year - $25,970 with a 7.25% depreciation = 25970 * 7.25% =1883 - 25970 = $24,087

Third Year - $24,087 with a 7.25% depreciation = 24087 * 7.25% = 1746 - 24087 = $22,341

Fourth Year = $22,341 with a 7.25% depreciation = 1620 - 22341 = $20,721

Fifth Year = $20.721 with a 7.25% depreciation = 1502 - 20721 = $19,219

carlosego

For this case we have a function of the form:

\(y = A * (b) ^ x
\)

Where,

A: initial value

b: decrease rate

x: time in years

Substituting values we have:

\(y = 28000 * (0.9275) ^ x
\)

For the year number 5 we have:

\(y = 28000 * (0.9275) ^ 5

y = 19219
\)

Answer:

the value of the car 5 years after it is purchased will be:

\(y = 19219\)

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