To find the value of the car after three years using the depreciation model \(f(x) = 32,000(0.92)^x\), we will substitute \(x = 3\) into the equation.
Calculating \(f(3)\):
\[ f(3) = 32,000(0.92)^3 \]
Now we need to calculate \(0.92^3\):
\[ 0.92^3 = 0.778688 \]
Now substituting this value in:
\[ f(3) = 32,000 \times 0.778688 \] \[ f(3) \approx 24,956.00 \]
So, the value of the car after three years, rounded to the nearest cent, is approximately $24,956.00.
Updating the table:
| x | f(x) | |---|------------| | 0 | $32,000.00 | | 1 | $29,440.00 | | 2 | $27,048.80 | | 3 | $24,956.00 |