To find the value of the car after 5 years using the given function \( f(x) = 35,000(0.85)^x \), we will evaluate the function at \( x = 5 \):
\[ f(5) = 35,000(0.85)^5 \]
First, we need to calculate \( (0.85)^5 \):
\[ (0.85)^5 \approx 0.443705 \]
Now, multiply this value by 35,000:
\[ f(5) \approx 35,000 \times 0.443705 \approx 15529.775 \]
Rounding to the nearest cent:
\[ f(5) \approx 15,529.78 \]
Therefore, rounded to the nearest cent, after 5 years, the value of the car will equal $15,529.78.