Brianna bought her car for $15,640. it is expected to depreciate an average of 15% each year during the first 7 years. what will the approximate value of her car be in 7 years?

a. $4898
b. $5014
c. $5108
d. $5146

First, lets talk through the logic here...

The car has an initial value of P. Each year it depreciates by 15%, which means it is now worth 85% of the original value, P (Since 100%-15% = 85%). This continues to happen each year. To find the value of the car in 7 years, we need to take into account 7 years of depreciation.

Value Year 2 = .85 (Value Year 1)
Value Year 3 = .85 (Value Year 2) = .85 (.85 (Value Year 1))
Value Year 4 = .85 (Value Year 3) = .85 (.85 ( .85 (Value Year 1))

Continue this same pattern until you have :

Value Year 7 = .85 (.85 (.85 (.85 (.85 (.85 (.85 (Value Year 1 = .85^7 (Value Year 1)

We can make this final simplification since multiplication is commutative. 

From the problem, Value Year 1 = $15,640. Therefore,

Value Year 7 = .85^7 (15640) ~ $5014