Acar loses 15% of its value per year. after how many years will a $28,000 car be worth $6,600? ( show work)

 approximately 8.89 years 

Explanation: Let 



Since the car loses 15% of the value after one year, 

New value of car after one year = (previous value) - (15% of previous value)
New value of car after one year = (previous value) - 0.15 × (previous value)
New value of car after one year = 0.85 × (previous value)      (1)

Based on our representation, if represents the new value, then  represents the previous value. Using equation (1),

            (2)

Moreover, note that represents the initial value of the car. So, using equation (2),




.
.
.

So, doing this for n times, we have 

   (3)

In the problem, the initial value of the car is $28,000 and we need to find the value of n such that after n years the value of the car is $6,600. 

So, . Using equation (3),