A car is purchased for $26,000. Each year it loses 25% of its value. After how many years will the car be worth $8400 or less? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.
Question
A car is purchased for 8400 or less? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.
Solution
Step 1: Understand the problem. The car loses 25% of its value each year. We need to find out how many years it will take for the car to be worth $8400 or less.
Step 2: Set up the equation. The car's value decreases by 25% each year, so we can represent the car's value after n years as 26000*(0.75)^n.
Step 3: Solve the equation. We want to find the smallest whole number n such that 26000*(0.75)^n <= 8400.
Step 4: Use trial and error to find the smallest whole number n that satisfies the equation.
- For n=1, 26000*(0.75)^1 = 19500, which is more than 8400.
- For n=2, 26000*(0.75)^2 = 14625, which is more than 8400.
- For n=3, 26000*(0.75)^3 = 10968.75, which is more than 8400.
- For n=4, 26000*(0.75)^4 = 8226.56, which is less than 8400.
So, it will take 4 years for the car to be worth $8400 or less.
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