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In the year 2009, a person bought a new car for
$17000. For each consecutive year after that, the value of the car depreciated by
8%. How much would the car be worth in the year 2011, to the nearest hundred dollars?
Answer:

In the year $2009$ , a person bought a new car for $\$ 17000$ . For each consecutive year after that, the value of the car depreciated by $8 \%$ . How much would the car be worth in the year $2011$ , to the nearest hundred dollars? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. In the year

2009

, a person bought a new car for

\$ 17000

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

8 \%

. How much would the car be worth in the year

2011

, to the nearest hundred dollars?

\newline

Answer:

Determine initial value and rate: Determine the initial value of the car and the annual depreciation rate. $\newline$ The initial value of the car, $P$ , is $\$17000$ , and the annual depreciation rate, $r$ , is $8\%$ .
Convert rate to decimal: Convert the annual depreciation rate from a percentage to a decimal. $\newline$ To convert $8\%$ to a decimal, divide by $100$ : $r = \frac{8}{100} = 0.08$ .
Calculate value after one year: Calculate the value of the car after one year. $\newline$ The value of the car after one year is given by $P \times (1 - r)$ . $\newline$ Substitute $P = 17000$ and $r = 0.08$ : $\newline$ Value after one year = $17000 \times (1 - 0.08) = 17000 \times 0.92$ .
Perform calculation for one year: Perform the calculation for the value after one year. $\newline$ Value after one year = $17000 \times 0.92 = 15640$ .
Calculate value after two years: Calculate the value of the car after two years. $\newline$ The value of the car after two years is given by the value after one year multiplied by $(1 - r)$ again. $\newline$ Value after two years = $15640 \times (1 - 0.08) = 15640 \times 0.92$ .
Perform calculation for two years: Perform the calculation for the value after two years. $\newline$ Value after two years = $15640 \times 0.92 = 14388.8$ .
Round value to nearest hundred: Round the value to the nearest hundred dollars. $\newline$ The value of the car in the year $2011$ , rounded to the nearest hundred dollars, is approximately $\$14400$ .

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