To find the value of the car after three years using the given equation \( f(x) = 32,000(0.92)^x \):
- Set \( x = 3 \) (since we're calculating the value after three years).
- Substitute \( x \) into the equation:
\[ f(3) = 32,000(0.92)^3 \]
- Calculate \( (0.92)^3 \):
\[ (0.92)^3 \approx 0.778688 \]
- Now, substitute this value back into the equation:
\[ f(3) = 32,000 \times 0.778688 \approx 24,916.00 \]
Rounding to the nearest cent gives us:
\[ f(3) \approx 24,916.00 \]
Therefore, the value of the car after three years is approximately $24,916.00. Since this may not match the given options exactly due to rounding, it looks like the closest option would be $24,918.02.
So the value of the car after three years is $24,918.02.
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