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

Let's perform the calculation:

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

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

\[ (0.85)^5 \approx 0.4437053125 \]

Now, substitute this value back into the function:

\[ f(5) = 35,000 \cdot 0.4437053125 \approx 15529.67659375 \]

Rounding this to the nearest cent gives us:

\[ f(5) \approx 15,529.68 \]

Therefore, rounded to the nearest cent, after 5 years, the value of the car will equal $15,529.68.