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 $

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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

Calculating \( f(5) \):

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

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

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

Now multiply this value by 35,000:

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

Rounding this value to the nearest cent gives:

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

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