SOLUTION: Every 13 months the value of a stock is one-third of its previous value. To the nearest month, when will the stock reach 6% of its original value?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Every 13 months the value of a stock is one-third of its previous value. To the nearest month, when will the stock reach 6% of its original value?      Log On


   

Question 1157426: Every 13 months the value of a stock is one-third of its previous value. To the nearest month, when will the stock reach 6% of its original value?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +v+ = the original value of the stock
Let +t+ = time in months the stock is held
+%28+6%2F100+%29%2Av+=+v%2A%28+1%2F3+%29%5E%28+t%2F13+%29+
+%28+3%2F50+%29%2Av+=+v%2A%28+1%2F3+%29%5E%28+t%2F13+%29+
Multiply both sides by +3%2A50+
+9v+=+150v%2A+%28+1%2F3+%29%5E%28+t%2F13+%29+
+9%2F150+=+%28+1%2F3+%29%5E%28+t%2F13+%29+
Take the log of both sides
+log%28+.06+%29+=+%28+t%2F13+%29%2A+log%28+.333+%29+
+-1.2218+=+%28+t%2F13+%29%2A%28+-.47712+%29+
+t%2F13+=+1.2218+%2F+.47712+
+t%2F13+=+2.56088+
+t+=+33.29+
+.29%2A30+=+9+
In about 33 months and 9 days
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check:
+%28+6%2F100+%29%2Av+=+v%2A%28+1%2F3+%29%5E%28+t%2F13+%29+
++.06++=+%28+1%2F3+%29%5E%28+33.29%2F13+%29+
+.06+=+%28+.333+%29%5E2.5609+
+.06+=+.059998+
close enough
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check the math
& get a 2nd opinion if needed