A car is purchased for $\$ 30,000$. Each year it loses $25 \%$ of its value. After how many years will the car be worth $\$ 9200$ or less? (Use the calcul necessary.)
Write the smallest possible whole number answer.
$\square$ years
\[
\times \quad 5
\]
Answer
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.
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.
