Question

A car decreases in value after a given number of years. The following function represents the value of the car in dollars with respect to its age, x, in years: f(x)=35,000(.85)^x
. Use the input-output table to determine the value of the car after 5 years. Round your answer to the nearest cent.

Answer 1

To determine the value of the car after 5 years using the given function \( f(x) = 35,000(0.85)^x \), we can substitute \( x = 5 \) into the function:

\[
f(5) = 35,000(0.85)^5
\]

Now we will calculate \( (0.85)^5 \):

\[
(0.85)^5 \approx 0.4437
\]

Next, we multiply this result by 35,000:

\[
f(5) = 35,000 \times 0.4437 \approx 15529.5
\]

Thus, the value of the car after 5 years is approximately \( 15529.5 \).

Rounding to the nearest cent, the final answer is:

\[
\boxed{15529.50}
\]