A car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. How much will the car be worth in 9 years?

Question

If necessary, round your answer to the nearest cent.

Answer 1

To determine the value of the car after 9 years, we can use the formula for exponential decay:

\[ V = P \times (1 - r)^t \]

Where:

• \( V \) is the future value of the car
• \( P \) is the initial price of the car
• \( r \) is the rate of depreciation per year (as a decimal)
• \( t \) is the number of years

Given:

• \( P = 43,330 \)
• \( r = 0.17 \) (17% loss in value)
• \( t = 9 \)

Substituting these values into the formula:

\[ V = 43,330 \times (1 - 0.17)^9 \]

Calculating \( (1 - 0.17) \):

\[ 1 - 0.17 = 0.83 \]

Now, we raise \( 0.83 \) to the power of \( 9 \):

\[ (0.83)^9 \approx 0.42241 \]

Now, multiply this result by the initial price:

\[ V \approx 43,330 \times 0.42241 \approx 18,325.27 \]

Thus, the value of the car after 9 years will be approximately $18,325.27.