Question

A car is purchased for $20,000. Each year it loses 30% of its value. After how many years will the car be worth $3400 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Answer 1

The car will be worth $3400 or less after 5 years.

Step-by-step explanation:

To find out after how many years the car will be worth $3400 or less, we need to determine when the value of the car depreciates to that amount.

Each year, the car loses 30% of its value, which means it retains 70% of its value. We can write this as:

Value after each year = 0.7 * Previous year's value

We can use this formula to calculate the value of the car each year until it reaches $3400 or less.

Let's do the calculations:

Year 1 = 0.7 * $20,000 = $14,000

Year 2 = 0.7 * $14,000 = $9,800

Year 3 = 0.7 * $9,800 = $6,860

Year 4 = 0.7 * $6,860 = $4,802

Year 5 = 0.7 * $4,802 = $3,361.40

After 5 years, the value of the car will be worth $3361.40, which is $3400 or less. Therefore, the car will be worth $3400 or less after 5 years.