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In the year 2004, a person bought a new car for
$28000. For each consecutive year after that, the value of the car depreciated by
13%. How much would the car be worth in the year 2007 , to the nearest hundred dollars?
Answer:

In the year $2004$ , a person bought a new car for $\$ 28000$ . For each consecutive year after that, the value of the car depreciated by $13 \%$ . How much would the car be worth in the year $2007$ , to the nearest hundred dollars? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. In the year

2004

, a person bought a new car for

\$ 28000

. For each consecutive year after that, the value of the car depreciated by

13 \%

. How much would the car be worth in the year

2007

, to the nearest hundred dollars?

\newline

Answer:

Determine Depreciation Factor: Determine the depreciation factor. $\newline$ The car depreciates by $13\%$ each year, which means it retains $87\%$ of its value each year ( $100\% - 13\% = 87\%$ ). $\newline$ The depreciation factor is $0.87$ ( $87\%$ expressed as a decimal).
Calculate Value After One Year: Calculate the value of the car after one year. $\newline$ The initial value of the car is $\$28000$ . $\newline$ After one year, the value is $\$28000 \times 0.87$ .
Perform Calculation for One Year: Perform the calculation for one year. $\$28000 \times 0.87 = \$24360.$
Repeat Depreciation Process: Repeat the depreciation process for each consecutive year. We need to apply the depreciation factor for three years ( $2004$ to $2007$ ).
Calculate Value After Second Year: Calculate the value of the car after the second year. $\newline$ Take the value from the first year and multiply by the depreciation factor again. $\newline$ $\$24360 \times 0.87 = \$21193.20$ .
Calculate Value After Third Year: Calculate the value of the car after the third year. $\newline$ Take the value from the second year and multiply by the depreciation factor once more. $\newline$ $\$21193.20 \times 0.87 = \$18438.08$ .
Round Final Value: Round the final value to the nearest hundred dollars. $\newline$ The value of the car in $2007$ is approximately $\$18400$ when rounded to the nearest hundred.

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