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In the year 2004 , a person bought a new car for
$15500. For each consecutive year after that, the value of the car depreciated by
10%. 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 $\$ 15500$ . For each consecutive year after that, the value of the car depreciated by $10 \%$ . 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

\$ 15500

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

10 \%

. How much would the car be worth in the year

2006

, 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 $\$15500$ , and the annual depreciation rate, $r$ , is $10\%$ .
Convert rate to decimal: Convert the annual depreciation rate to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 10\% = \frac{10}{100} = 0.10$
Calculate value after $1$ year: Calculate the value of the car after one year. $\newline$ The value of the car after one year is found by subtracting $10$ % of its value. $\newline$ Value after $1$ year = $P \times (1 - r)$ $\newline$ = $\$15500 \times (1 - 0.10)$ $\newline$ = $\$15500 \times 0.90$ $\newline$ = $\$13950$
Calculate value after $2$ years: Calculate the value of the car after two years. $\newline$ The value of the car after two years is found by applying the depreciation rate again to the value after one year. $\newline$ Value after $2$ years = Value after $1$ year * $(1 - r)$ $\newline$ = $\$13950$ * $(1 - 0.10)$ $\newline$ = $\$13950$ * $0$ . $90$ $\newline$ = $\$12555$
Round to nearest hundred: Round the value to the nearest hundred dollars. $\newline$ To round to the nearest hundred, look at the tens digit. If it is $5$ or more, round up. If it is $4$ or less, round down. $\newline$ The tens digit of $\$12555$ is $5$ , so we round up. $\newline$ Rounded value = $\$12600$

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