.
A photocopier was purchased for $12500. The value of the machine each year is 85%
of its value the preceding year.
To the nearest tenth of a year, how long will it take before it is worth only $1500?
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A function which describes the value of this item is this exponential function
V(t) = ,
where V(t) is the current value; is the original value at t= 0; t is the time in years.
To find "t", we write
1500 = .
Then we divide both sides by 12500
=
or
0.12 = .
Next, we take logarithm base 10 of both sides
log(0.12) = t*log(0.85)
and express
t = = 13.0463 years.
You may round it to 13.0 years, as requested. ANSWER
Solved.
It is a standard procedure for solving such problems.
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To see many other similar (and different) solved problems, look into the lesson
- Problems on appreciated/depreciated values
in this site.
Learn the subject from there.