Question

When a certain car is initially purchased, its value is 20,000 dollars. If the car loses 9% of its value each year, when will the car's value be 10,000 dollars?

(A) Between the date of the initial purchase and 1 year
(B) Between 7 years and 8 years after its initial purchase
(C) Between 1 year and 2 years after its initial purchase
(D) Between 5 years and 6 years after its initial purchase

Answer 1

It will take approximately 5.56 years for the car's value to be $10,000, which falls between 5 years and 6 years after its initial purchase. The correct answer is option D.

Step-by-step explanation:

To solve this problem, we can set up an equation. Let x represent the number of years it takes for the car's value to be $10,000. Since the car loses 9% of its value each year, we can write the equation:

$20,000 - 0.09($20,000)(x) = $10,000

Simplifying the equation, we get:

$20,000 - 0.09(20,000x) = 10,000

$20,000 - 1,800x = 10,000

Subtracting $20,000 from both sides, we get:

-1,800x = -10,000

Dividing both sides by -1,800, we get:

x = 5.5

Therefore, it will take approximately 5.56 years for the car's value to be $10,000. Since this is between 5 years and 6 years, the answer is (D) Between 5 years and 6 years after its initial purchase.