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