Question

The value of a $25,000 car decreases by 9% each year. Use an equation to find is the car's approximate value after 5 years. (1 point)

$12,500

$0.15

$22,500

$15,601

Answer 1

To find the approximate value of the car after 5 years, we can use the formula for exponential decay:

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

where:
- \( V \) is the future value of the car,
- \( P \) is the initial value of the car ($25,000),
- \( r \) is the rate of decrease (9% or 0.09),
- \( t \) is the time in years.

Plugging in the values:

\[
V = 25000(1 - 0.09)^5
\]

Calculating this step-by-step:

1. Calculate \( (1 - 0.09) = 0.91 \).
2. Now raise \( 0.91 \) to the power of 5:

\[
0.91^5 \approx 0.6598
\]

3. Now multiply by the initial value:

\[
V \approx 25000 \times 0.6598 \approx 16494.5
\]

So, the approximate value of the car after 5 years is about \$16,494.5.

Among the options given, none exactly match this value, but the closest answer is **$15,601**.