SOLUTION: The value of a machine, V, at the end of t years is given by V=C(1-r)^t , where C is the original cost of the machine and r is the rate of depreciation. A machine that originally c

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The value of a machine, V, at the end of t years is given by V=C(1-r)^t , where C is the original cost of the machine and r is the rate of depreciation. A machine that originally c      Log On


   

Question 1041740: The value of a machine, V, at the end of t years is given by V=C(1-r)^t , where C is the original cost of the machine and r is the rate of depreciation. A machine that originally cost $17,800 is now valued at $9,547. How old is the machine if r=0.17?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
V=C%281-r%29%5Et

log%28%28V%29%29=log%28%28C%29%29%2Blog%28%28%281-r%29%5Et%29%29

log%28%28V%29%29=log%28%28C%29%29%2Bt%2Alog%28%281-r%29%29

t%2Alog%28%281-r%29%29=log%28%28V%29%29-log%28%28C%29%29

t=%28log%28%28V%29%29-log%28%28C%29%29%29%2Flog%28%281-r%29%29

Substitute the given values.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

The value of a machine, V, at the end of t years is given by V=C(1-r)^t , where C is the original cost of the machine and r is the rate of depreciation. A machine that originally cost $17,800 is now valued at $9,547. How old is the machine if r=0.17?
With "t" being age, in years, we get:  = highlight_green%28matrix%281%2C2%2C+3.343384847%2C+years%29%29