# exponentil fraction

#### porterehd

##### New member
A new car is purchased for 17000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 12 years?

#### skeeter

##### Elite Member
How would you determine the value after ...

1 year?
2 years?
.
.
.
t years?

10 years

#### Otis

##### Elite Member
exponentil fraction
The value of the car depreciates at 13.5% per year.
Hi porterehd. You've posted on the Pre-Algebra board. Has your class been discussing exponential fractions? If so, then how do they define those?

Otherwise, do you know how to calculate (100-13.5)% of 17000 ?

#### HallsofIvy

##### Elite Member
If a car has value V and depreciates at a% per year (so a/100) then after one year its value has lowered by V(a/1000)= aV/100 so is now V- aV/100=(100V- aV)/100A= [(100- a)/100]V. That is, V has been multiplied by (100- a)/100. The second year, the same thing happens- its value, now [(100- a)/100]V, is again multiplied by (100- a)/100 so after the second year the value is [(100- a)/100]^2V.

The third you again multiply by (100- a)/100. What will the value be after the third year? The fourth year? Get the point?