SOLUTION: If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n=f(t)=100(2 to the t/3 power). When will the populati

Question 177896: If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n=f(t)=100(2 to the t/3 power). When will the population reach 50,000?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n=f(t)=100(2 to the t/3 power). When will the population reach 50,000?
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50,000 = 100(2)^(t/3)
2^(t/3) = 500
Take the log of both sides to get:
(t/3)log2 = log500
t/3 = log(500)/log(2)
t/3 = 8.9657..
t = 26.9 hours
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Cheers,
Stan H.
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