SOLUTION: After 8 years, a car depreciated to $12,000 from its original purchase price. If it depreciated by 6% per year, what was the original price? Do you use this formula A=a(1+r)^t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: After 8 years, a car depreciated to $12,000 from its original purchase price. If it depreciated by 6% per year, what was the original price? Do you use this formula A=a(1+r)^t      Log On


   

Question 728608: After 8 years, a car depreciated to $12,000 from its original purchase price. If it depreciated by 6% per year, what was the original price?

Do you use this formula A=a(1+r)^t? And how would you set it up?
Answer by ohtheirony(35) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for exponential growth is A=a%281%2Bx%29%5Et. However, the car value is depreciating, making this an exponential decay problem. The equation for exponential decay is A=a%281-x%29%5Et.


a=the original starting rate (the price of the car:$12,000)
x=percent the rate is increasing/decreasing annually (depreciation of 6%)
t=amount of time past while the amount is increasing/decreasing (8 years)


So, your equation would be...
A=a%281-x%29%5Et
A=12,000(1-.06)^8 (^8 is (1-.06) to the eighth exponent)
A=12,000(.94)^8
A=12,000(.609568939)
A=7314.82726


The car will be $7,314.83 in 8 years. The numbers in exponential growth and decay will often be long. I tend to use the whole number displayed on the calculator and do not round until the very end. However, read the directions carefully to see how to round your answer in between steps.


For more on exponential growth/decay, try this link:
http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/ExpDecayL.htm