To find the value of the car after three years using the depreciation model \( f(x) = 32,000(0.92)^x \), we can substitute \( x = 3 \):
\[ f(3) = 32,000(0.92)^3 \]
First, we calculate \( (0.92)^3 \):
\[ 0.92^3 = 0.7792 \quad (\text{approximately}) \]
Now, multiply this value by 32,000:
\[ f(3) = 32,000 \times 0.7792 \]
Calculating that gives us:
\[ f(3) = 32,000 \times 0.7792 = 24,942.40 \]
Thus, the value of the car after three years is approximately $24,942.40.