SOLUTION: approximately one half of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. the number in use after t years is given by the

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Question 301785: approximately one half of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. the number in use after t
years is given by the function. N(t)=310,000(1/2)^t.
How many years will 5000 bottles still be in use?
I've tried several different ways to work this function and get a different answer every time!!!!!! Do Ineed to replace N for the 5000 to solve?
Thanks,
Desperately Trying

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
N%28t%29+=+310000%2A%281%2F2%29%5Et
5000+=+310000%2A%281%2F2%29%5Et
Multiply both sides by 2%5Et
2%5Et+=+310000%2F5000
2%5Et+=+62
take the log of both sides
log%282%5Et%29+=+log%2862%29
t%2Alog%282%29+=+log%2862%29
t+=+log%2862%29%2Flog%282%29
You can solve with calculator