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In the year 2004, a person bought a new car for
$16000. For each consecutive year after that, the value of the car depreciated by
13%. How much would the car be worth in the year 2006, to the nearest hundred dollars?
Answer:

In the year $2004$ , a person bought a new car for $\$ 16000$ . For each consecutive year after that, the value of the car depreciated by $13 \%$ . How much would the car be worth in the year $2006$ , 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

\$ 16000

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

13 \%

. How much would the car be worth in the year

2006

, to the nearest hundred dollars?

\newline

Answer:

Determine Initial Value and Depreciation Rate: Determine the initial value of the car and the annual depreciation rate. $\newline$ The initial value of the car is $\$16,000$ , and it depreciates by $13\%$ each year.
Calculate Value After Year $1$ : Calculate the value of the car after one year ( $2005$ ). $\newline$ The value after one year is the initial value minus the depreciation. $\newline$ Depreciation for one year is $13$ \% of $\$16,000$ . $\newline$ Depreciation = $0.13 \times \$16,000 = \$2,080$ . $\newline$ Value after one year = $\$16,000 - \$2,080 = \$13,920$ .
Calculate Value After Year $2$ : Calculate the value of the car after the second year ( $2006$ ). The value after the second year is the value after the first year minus the second year's depreciation. Depreciation for the second year is $13$ \% of $\$13,920$ . Depreciation = $0.13 \times \$13,920 = \$1,809.60$ . Value after the second year = $\$13,920 - \$1,809.60 = \$12,110.40$ .
Round Value to Nearest Hundred: Round the value to the nearest hundred dollars. $\newline$ The value of the car in $2006$ rounded to the nearest hundred dollars is approximately $\$12,100$ .

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