Years, x | Value of Car, f (x)

Question

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

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

Now we need to calculate \( (0.85)^5 \):

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

Now substitute this value back into the function:

\[ f(5) = 35,000 \times 0.4437053125 \]

Calculating this gives:

\[ f(5) \approx 35,000 \times 0.4437053125 \approx 15,033.65 \]

Therefore, the value of the car after 5 years is approximately $15,033.65 when rounded to the nearest cent.