Use the table to answer the question.

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.

Answer 1

To find the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we need to substitute \( x = 5 \) into the function.

Calculating \( f(5) \):

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

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

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

Next, we multiply this by 35,000:

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

Rounding to the nearest cent, we get:

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

So, the value of the car after 5 years is approximately $15,529.78.