The general formula is $y=a(b)^{x}$. In this case $y$ is the value of the car, $x$ is the time in years, $a=32,000$ is the starting amount in thousands, and $b=0.85$ since we multiply the value in any year by this factor to get the value of the car in the following year. The formula for this problem is:
\[
y=32000
\]
Finally, to find the value of the car when it is four years old, we use $x=4$ in the formula. Remember the value is in thousands.
\[
y=32000(0.85)^{4}=16,704.2
\]
At 4 years old, we expect the car to be worth $\$ 16700$

Step 1 ：The general formula for exponential decay is given by \(y=a(b)^{x}\). In this context, 'y' represents the value of the car, 'x' is the time in years, 'a' is the initial value of the car, and 'b' is the decay factor.

Step 2 ：In this problem, the initial value of the car 'a' is $32,000, and the decay factor 'b' is 0.85. This means that the value of the car decreases by 15% each year.

Step 3 ：We are asked to find the value of the car after 4 years. To do this, we substitute 'a' = 32000, 'b' = 0.85, and 'x' = 4 into the formula.

Step 4 ：Substituting these values into the formula gives \(y=32000(0.85)^{4}\).

Step 5 ：Solving this equation gives \(y=16704.2\). This means that the value of the car after 4 years is approximately $16,704.20.

Step 6 ：\(\boxed{The value of the car after 4 years is approximately $16,704.20.}\)