For each one-year period after a car was purchased, its value at the end of the year was 15% less than its value at the beginning of the year. If the value of the car 2 years after it was bought is $17,918, what was the value of the car when it was bought?
Let's call the value of the car when it was bought "x".
After one year, the value of the car would be 0.85x (15% less than x).
After two years, the value of the car would be 0.85(0.85x) = 0.7225x (15% less than 0.85x).
We know that this value is equal to $17,918:
0.7225x = $17,918
To solve for x, we need to divide both sides by 0.7225:
x = $24,750
Therefore, the value of the car when it was bought was $24,750.
Let's assume the value of the car when it was bought was V dollars.
After 1 year, the value of the car would be 85% of V, which is (0.85)(V) dollars.
After 2 years, the value of the car would be 85% of the value after 1 year, which is (0.85)((0.85)(V)) dollars.
Given that the value of the car 2 years after it was bought is $17,918, we can set up the equation:
(0.85)((0.85)(V)) = $17,918
Simplifying this equation, we have:
0.7225V = $17,918
Now, let's solve for V by dividing both sides of the equation by 0.7225:
V = $17,918 / 0.7225
V ≈ $24,806.50
Therefore, the value of the car when it was bought was approximately $24,806.50.