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.

Question

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 \( f(x) = 35000(0.85)^x \), we can plug in \( x = 5 \):

\[ f(5) = 35000(0.85)^5 \]

First, we need to calculate \( (0.85)^5 \):

\[ (0.85)^5 \approx 0.4437 \quad (\text{rounded to four decimal places}) \]

Now we can calculate \( f(5) \):

\[ f(5) = 35000 \times 0.4437 \approx 15529.5 \]

Finally, rounding to the nearest cent, the value of the car after 5 years will be:

\[ \text{Value} = 15529.50 \]

Thus, the answer is:

$15,529.50