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.

(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 function \( f(x) = 35,000 \times (0.85)^x \), we substitute \( x = 5 \) into the function.

Calculating \( f(5) \):

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

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

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

Now we multiply this result by 35,000:

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

Rounding this to the nearest cent, we have:

\[ f(5) \approx 15529.78 \]

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