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eview Unit 6
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Question
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A new car is purchased for 17300 dollars. The value of the car depreciates at
9.25% pe year. What will the value of the car be, to the nearest cent, after 15 years?
Answer Attempt 1 out of 2

eview Unit $6$ $\newline$ Score: $2 / 10$ $\newline$ Penalty: $1$ off $\newline$ Question $\newline$ Show Examples $\newline$ A new car is purchased for $17300$ dollars. The value of the car depreciates at $9.25 \%$ pe year. What will the value of the car be, to the nearest cent, after $15$ years? $\newline$ Answer Attempt $1$ out of $2$

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Exponential growth and decay: word problems

Full solution

Q. eview Unit

6

\newline

Score:

2 / 10

\newline

Penalty:

1

off

\newline

Question

\newline

Show Examples

\newline

A new car is purchased for

17300

dollars. The value of the car depreciates at

9.25 \%

pe year. What will the value of the car be, to the nearest cent, after

15

years?

\newline

Answer Attempt

1

out of

2

Identify values: Identify the initial value of the car and the annual depreciation rate. $\newline$ The initial value of the car is $\$17,300$ , and it depreciates at a rate of $9.25\%$ per year.
Convert to decimal: Convert the annual depreciation rate from a percentage to a decimal. $\newline$ To convert $9.25\%$ to a decimal, divide by $100$ . $\newline$ $9.25\% / 100 = 0.0925$
Determine factor: Determine the depreciation factor. $\newline$ The depreciation factor is $1$ minus the depreciation rate. $\newline$ Depreciation factor = $1 - 0.0925 = 0.9075$
Apply formula: Apply the depreciation factor over $15$ years to find the car's value. $\newline$ The formula for depreciation is: $\newline$ Final Value $=$ Initial Value $\times$ (Depreciation Factor) $^{\text{Number of Years}}$
Calculate value: Calculate the value of the car after $15$ years. $\newline$ Final Value = $\$17,300 \times (0.9075)^{15}$
Perform calculation: Perform the calculation. $\newline$ Final Value = $\$17,300 \times (0.9075)^{15}$ $\newline$ Final Value $\approx \$17,300 \times 0.2776$ (rounded to four decimal places) $\newline$ Final Value $\approx \$4,803.48$
Round final value: Round the final value to the nearest cent. $\newline$ The value of the car after $15$ years, rounded to the nearest cent, is approximately $\$4,803.48$ .

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