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Emma pays $\$2,600$ for a washer/dryer combo. Each year, the appliance loses $15\%$ of its resale value. How much will it be worth in $4$ years? If necessary, round your answer to the nearest cent. $\newline$ $\$$ ____

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Exponential growth and decay: word problems

Full solution

Q. Emma pays

\$2,600

for a washer/dryer combo. Each year, the appliance loses

15\%

of its resale value. How much will it be worth in

4

years? If necessary, round your answer to the nearest cent.

\newline

\$

____

Determine initial value and rate: Determine the initial value and the depreciation rate. $\newline$ The initial value of the washer/dryer combo is $\$2,600$ , and it depreciates by $15\%$ each year.
Understand depreciation process: Understand the depreciation process. $\newline$ Depreciation means the value decreases by a certain percentage each year. In this case, the washer/dryer combo retains $85\%$ of its value each year ( $100\% - 15\% = 85\%$ ).
Convert percentage to decimal: Convert the percentage to a decimal to use in calculations. $\newline$ $15\%$ as a decimal is $0.15$ , so the washer/dryer combo retains $85\%$ of its value, which is $1 - 0.15 = 0.85$ as a decimal.
Calculate value after one year: Calculate the value after one year. $\newline$ After one year, the value of the washer/dryer combo is $\$2,600 \times 0.85$ . $\newline$ $\$2,600 \times 0.85 = \$2,210$ .
Calculate value after two years: Calculate the value after two years. $\newline$ After two years, the value is $\$2,210 \times 0.85$ . $\newline$ $\$2,210 \times 0.85 = \$1,878.50$ .
Calculate value after three years: Calculate the value after three years. $\newline$ After three years, the value is $\$1,878.50 \times 0.85$ . $\newline$ $\$1,878.50 \times 0.85 = \$1,596.725$ .
Calculate value after four years: Calculate the value after four years. $\newline$ After four years, the value is $\$1,596.725 \times 0.85$ . $\newline$ $\$1,596.725 \times 0.85 = \$1,357.21625$ .
Round final value: Round the final value to the nearest cent. $\newline$ The value of the washer/dryer combo after four years, rounded to the nearest cent, is $\$1,357.22$ .

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