SOLUTION: a machine depreciates in value each year by 8% of its value at the beginning of the year. After how many years will its value first be less than half its original value?

Algebra ->  Sequences-and-series -> SOLUTION: a machine depreciates in value each year by 8% of its value at the beginning of the year. After how many years will its value first be less than half its original value?      Log On


   



Question 982141: a machine depreciates in value each year by 8% of its value at the beginning of the year. After how many years will its value first be less than half its original value?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +V+ = it's original value
Let +V%2F2+ = it's final value
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Let +n+ = number of years until
+V+ becomes +V%2F2+
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+V%2F2+=+V%2A%28+1+-+.08+%29%5En+
Divide both sides by +V+
+1%2F2+=+%28+1+-+.08+%29%5En+
+1%2F2+=+.92%5En+
+log%28+.5+%29+=+n%2Alog%28+.92+%29+
+n+=+log%28+.5+%29+%2F+log%28+.92+%29+
+n+=+.30103+%2F+.03621+
+n+=+8.3134+
At the end of the 8th year, the value will
be less than 1/2 of it's original value
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check:
+1%2F2+=+.92%5En+
+.5+=+.92%5E8.3134+
+.5+=+.49998+
close enough