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:

$$\boxed{{\displaystyle 15529.50}}$$