SOLUTION: Can you help with this logarithm question? I have never had a problem like this A color photocopier is purchased for $5200. its value each year is about 70% of its value in the pr

Question 458249: Can you help with this logarithm question? I have never had a problem like this
A color photocopier is purchased for $5200. its value each year is about 70% of its value in the preceding year. Its value after t years is given by the exponential function V(t)=5200(0.07)^t.
a) Find the salvage value of the copier after 3 yr.
b) After what amount of time will the salvage value be $1200.
c) After what amount of time will the salvage be half the original value?
Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A color photocopier is purchased for $5200. its value each year is about 70% of its value in the preceding year. Its value after t years is given by the exponential function V(t)=5200(0.70)^t.
---------------------------
a) Find the salvage value of the copier after 3 yr.
V(3) = 5200*0.70^3 = $1783
-------------------------------------
b) After what amount of time will the salvage value be $1200.
Solve: 1200 = 5200(0.70)^t
0.70^t = 3/13
Take the log of both sides:
t*log(0.70) = log(3/13)
---
t = log(3/13)/log(0.70)
t = 4.11 years
============================
c) After what amount of time will the salvage be half the original value?
That will happen when (0.70)^t = 1/2
Take the log of both sides and solve for "t":
t = log(1/2)/log(0.7)
t = 1.94 years
============================
Cheers,
Stan H.
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