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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (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?
---------------------
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
===================
Cheers,
Stan H.