Sydney bought a new car for $32,000.00. If the car depreciates in value by 8% each year, the situation can be modeled by the equation f(x)=32,000(0.92)x (1 point) The value of the car after three years is $ (to the nearest cent). Question 2

Answer 1

To find the value of the car after three years using the given depreciation model, we can substitute \( x = 3 \) into the equation:

\[ f(x) = 32,000(0.92)^x \]

Substituting \( x = 3 \):

\[ f(3) = 32,000(0.92)^3 \]

Calculating \( (0.92)^3 \):

\[ 0.92^3 \approx 0.778688 \]

Now, multiplying this by 32,000:

\[ f(3) = 32,000 \times 0.778688 \approx 24,996.00 \]

Thus, the value of the car after three years is approximately $24,996.00 (to the nearest cent).