Step 1 :The problem is asking for the number of years it will take for the car's value to depreciate to $9200 or less. The car's value depreciates by 25% each year. This is a problem of exponential decay.
Step 2 :We can set up the equation as follows: \(30000 \times (0.75)^n \leq 9200\), where n is the number of years. We can solve this equation for n.
Step 3 :By solving the equation, we find that n equals 5.
Step 4 :Final Answer: The smallest possible whole number of years it will take for the car's value to depreciate to $9200 or less is \(\boxed{5}\) years.