SOLUTION: Approximately one-half of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. The number still in use after t years is given b

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Question 338196: Approximately one-half of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. The number still in use after t years is given by the function N(t)=310,000(1/2)^t
After how many years will 5000 bottles still be in use?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Approximately one-half of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. The number still in use after t years is given by the function N(t)=310,000(1/2)^t
After how many years will 5000 bottles still be in use?
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Simply set N(t) to 5000 and solve for t:
+N%28t%29=310%2C000%281%2F2%29%5Et+
+5000+=+310000%281%2F2%29%5Et+
+5000%2F310000+=+%281%2F2%29%5Et+
+5%2F310+=+%281%2F2%29%5Et+
+1%2F62+=+%281%2F2%29%5Et+
+log%281%2F2%2C1%2F62%29+=+t+
applying change of base:
+log%281%2F62%29%2Flog%281%2F2%29+=+t+
6 years = t