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 plug in \( x = 5 \) into the function.

Here's the calculation:

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

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

\[ (0.85)^5 \approx 0.4437 \quad (\text{using a calculator}) \]

Now, multiply this result by 35,000:

\[ f(5) = 35,000 \times 0.4437 \approx 15,034.50 \]

Therefore, the value of the car after 5 years is approximately $15,034.50.