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. After 5 years, the value of the car will equal $?

Answer 1

To find the value of the car after 5 years using the given function \( f(x) = 35,000 \cdot (0.85)^x \), we will plug in \( x = 5 \).

Here’s the calculation:

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

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

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

Now multiply this by 35,000:

\[ f(5) = 35,000 \cdot 0.4437053125 \approx 15529.64659375 \]

Rounding to the nearest cent, the value of the car after 5 years is:

\[ f(5) \approx 15,529.65 \]

So after 5 years, the value of the car will equal $15,529.65.