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 purchased is $17,918, what was the value of the car when it was purchased? Show your work or explain your answer.
The value of the car when it was purchased can be found by using the equation V = V0(1-0.15)^2, where V is the value of the car 2 years after it was purchased, V0 is the value of the car when it was purchased, and 0.15 is the percentage decrease in value each year.
Plugging in the given values, we get:
17,918 = V0(1-0.15)^2
17,918 = V0(0.7)^2
17,918 = V0(0.49)
V0 = 17,918/0.49
V0 = 36,400
Therefore, the value of the car when it was purchased was $36,400.