SOLUTION: Please help really stumped! Approximately one-third of all glass bottles distributed will be recycled each year. A beverage company distributes 310,000 bottles. The number still in

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Question 248628: Please help really stumped! Approximately one-third 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 60,000 bottles still be in use?
.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st part of the problem seems to say that 2/3 of the bottles
are still in use after 1 year, but the formula seems to say that
1/2 of the bottles are still in use after 1 year. I'm stumped, too

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
310,000(1/2)^t = 60000
Divide both sides by 310000
%281%2F2%29%5Et = 60000%2F310000
:
%281%2F2%29%5Et = 6%2F31
log%28%281%2F2%29%5Et%29+=+log%286%2F31%29
t%2Alog%281%2F2%29+=+log%286%2F31%29
-.301t = -.713
t = %28-.713%29%2F%28-.301%29
t = +2.37 yrs
:
:
Check on a calc: enter: 31000 * .5^2.37 = 59968 ~ 60000
:
jos is right, when you get this contradiction resolved, you can use this method