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 function \( f(x) = 35,000 \cdot (0.85)^x \), we need to substitute \( x = 5 \) into the function:

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

First, we calculate \( (0.85)^5 \):

\[
(0.85)^5 \approx 0.4437053125
\]

Now, we can substitute this value back into the equation:

\[
f(5) = 35,000 \cdot 0.4437053125
\]

Calculating the multiplication:

\[
f(5) \approx 35,000 \cdot 0.4437053125 \approx 15529.64659375
\]

Finally, rounding to the nearest cent:

\[
f(5) \approx 15529.65
\]

Thus, the value of the car after 5 years is approximately **$15,529.65**.