Question

Use the table to answer the question.

Years, x Value of Car, f(x)

1 29, 750.00
2 25, 287.50
3 21, 494.38
4 18, 270.22
5 ?

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.

(1 point)
Rounded to the nearest cent, after 5 years, the value of the car will equal $
.

Answer 1

wrong

Answer 2

To find the value of the car after 5 years using the function \( f(x) = 35,000 \cdot (0.85)^x \), we will calculate \( f(5) \).

Substituting \( x = 5 \) into the function:

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

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

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

Now, we compute \( f(5) \):

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

Rounding to the nearest cent, the value of the car after 5 years is:

\[
\text{Rounded to the nearest cent, after 5 years, the value of the car will equal } \$15,529.50.
\]