1 29, 750.00

Question

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

To find the value of the car after 5 years using the given function \( f(x) = 35,000(0.85)^x \), we will evaluate the function at \( x = 5 \):

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

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

\[ (0.85)^5 \approx 0.443705 \]

Now, multiply this value by 35,000:

\[ f(5) \approx 35,000 \times 0.443705 \approx 15529.775 \]

Rounding to the nearest cent:

\[ f(5) \approx 15,529.78 \]

Therefore, rounded to the nearest cent, after 5 years, the value of the car will equal $15,529.78.