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In the year 2001, a person bought a new car for
$17000. For each consecutive year after that, the value of the car depreciated by
10%. How much would the car be worth in the year 2003 , to the nearest hundred dollars?
Answer:

In the year $2001$ , a person bought a new car for $\$ 17000$ . For each consecutive year after that, the value of the car depreciated by $10 \%$ . How much would the car be worth in the year $2003$ , to the nearest hundred dollars? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. In the year

2001

, a person bought a new car for

\$ 17000

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

10 \%

. How much would the car be worth in the year

2003

, 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 in $2001$ is $\$17000$ , and it depreciates by $10\%$ each year.
Calculate value in $2002$ : Calculate the value of the car after one year ( $2002$ ). $\newline$ To find the value after one year, we multiply the initial value by $90$ % (which is $100$ % - $10$ % depreciation). $\newline$ Value in $2002$ = $\$17000 \times 0.90$
Perform calculation for $2002$ : Perform the calculation for the value in $2002$ . $\newline$ Value in $2002$ = $\$17000 \times 0.90 = \$15300$
Calculate value in $2003$ : Calculate the value of the car after the second year ( $2003$ ). $\newline$ The value after the second year is found by multiplying the value after the first year by $90\%$ again. $\newline$ Value in $2003$ = $\$15300 \times 0.90$
Perform calculation for $2003$ : Perform the calculation for the value in $2003$ . $\newline$ Value in $2003$ = $\$15300 \times 0.90 = \$13770$
Round value to nearest hundred: Round the value to the nearest hundred dollars. $\newline$ The value of $\$13770$ rounded to the nearest hundred is $\$13800$ .

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