SOLUTION: Good morning. Please help me solve this question. Approximately .25 of all glass bottles distributed will be recycled each year. A beverage company distributes 390000 bottles. The

Question 1020461: Good morning. Please help me solve this question.
Approximately .25 of all glass bottles distributed will be recycled each year. A beverage company distributes 390000 bottles. The number still in use after t years is N(t)=390000(.5)^t. After how many years will 60000 bottles still be in use?
I think I'll need to solve for t and replace N(t) with 60000. I can not figure out how to solve for t when its the exponent. Please help. Thank you!
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
N(t) =390000(.5)^t
60000 = 390000(.5)^t
60000/390000 = (.5)^t
0.153846 = (.5)^t
log 0.153846 log(.5)^t
log 0.153846 = t log(.5)
t = log 0153846/log (.5)
t = 2.7
2.7 years
Hope this helps :-)
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