A car decreases in value after a given number of years. The following function represents the value of the car in dollers with respect to its age, x in years: f(x) =35, 000 .(8.5). Use the input-output to determine the value of the car after 5 years. Round your answer to the nearest cent.

Answer 1

The function given is:

\[ f(x) = 35000 \cdot (0.85)^x \]

To find the value of the car after 5 years, we need to calculate \( f(5) \):

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

Now, let's compute \( (0.85)^5 \):

\[ (0.85)^5 \approx 0.4437 \]

Now substitute this value back into the equation for \( f(5) \):

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

Thus, the value of the car after 5 years is approximately:

\[ \boxed{15529.50} \]