SOLUTION: Stereo System. You purchase a stereo system for $830. After a 3-month trial period, the value of the stereo system decreases 13% each year. a. Write an exponential decay model

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Stereo System. You purchase a stereo system for $830. After a 3-month trial period, the value of the stereo system decreases 13% each year. a. Write an exponential decay model       Log On


   

Question 65473: Stereo System. You purchase a stereo system for $830. After a 3-month trial period, the value of the stereo system decreases 13% each year.
a. Write an exponential decay model for the value of the stereo system in terms of the number of years since the purchase.
b. What was the value of the system after 1 year?
I thought it was 830(.87)^x... but how do I put in the model the part about it only starts decreasing AFTER 3 months???
Thanks very much,
E
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
V%5BT%5D+=+P%281+-+r%29%5ET
V%5BT%5D is the value after T years
P is the purchase price
r is the annual interest rate
T is number of years after the 3 month trial period
Note that T+%3E=+0 and T+=+0 is when the
3 month trial period has ended
T(years) = (t(months) - 3) / 12
Note that when t+=+3, T = 0 and V%28T%29+=+P%281+-+r%29%5ET+=+P
as it should.
When t+=+15, T+=+1 (1 year after trial)
and V(1) = 830%28.87%29
V(1) = 722.10
What is the value after 1 year? I assume this means 1 year after
purchase, not 1 year after the 3 month trial.
Set t+=+12 then T+=+%2812+-+3%29+%2F+12
T+=+9+%2F+12
T+=+3%2F4
V(3/4) = +830%281+-+.13%29%5E%283%2F4%29
V(3/4) = 830%28.87%29%5E%283%2F4%29
V(3/4) = 830+%2A+.900
V(3/4) = 747.68
So, the value after a year is $ 747.68