SOLUTION: A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed

Algebra ->  Finance -> SOLUTION: A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed       Log On


   

Question 614077: A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed since the equipment was purchased, and V(t) is in dollars. After how many years will the value of the equipment be $3300?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed since the equipment was purchased, and V(t) is in dollars. After how many years will the value of the equipment be $3300?
.
Given:
V%28t%29=13200%284%29%5E-0.14t
set V(t) t0 3300 and solve for t
3300=13200%284%29%5E-0.14t
%283300%2F13200%29=%284%29%5E-0.14t
0.25+=+%284%29%5E-0.14t
take log base 4 of both sides:
log%284%2C0.24%29+=+-0.14t
log%280.24%29%2Flog%284%29+=+-0.14t
log%280.24%29%2F%28-0.14log%284%29%29+=+t
7.35319+=+t
answer: 7.35 years