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

Question 301820: Approximately one-half of all glass bottles distributed will be recycled each yesr, 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 5,000 bottles still be in use?

Let N(t) = 5,000 and solve for t.
5,000 = 310,000(1/2)^(t)
I do not know how to solve it from here Please Help!!!!!
Answer by london maths tutor(243) (Show Source): You can put this solution on YOUR website!
N(t) = 310 000 (1/2) ^t
5000 = N(t)
5000 = 310 000 (1/2) ^t
5000/31000 = (1/2)^t
1/62 = (1/2)^t
Using log:
t = [ lg(1/62) ] / [ lg (1/2) ]
= 5.95 years
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