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

50.15

$22,500

$15,001

Answer 1

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

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

where:
- \( V \) = future value of the car
- \( P \) = initial value of the car
- \( r \) = rate of depreciation (as a decimal)
- \( t \) = time in years

For this car:
- \( P = 25,000 \)
- \( r = 0.09 \) (since 9% = 0.09)
- \( t = 5 \)

Substituting these values into the formula, we get:

\[
V = 25000(1 - 0.09)^5
\]
\[
V = 25000(0.91)^5
\]

Now, calculate \( (0.91)^5 \):

\[
(0.91)^5 \approx 0.6593
\]

Now substitute this back into our equation:

\[
V \approx 25000 \times 0.6593 \approx 16482.50
\]

Thus, the approximate value of the car after 5 years is around $16,482.50.

Among the options provided, the closest value is **$15,001**.