Math

The generation time G for a particular bacterium is the time it takes for the population to double. The bacteria increase in population is shown by the formula G = t over 3.3log a p, where t is the time period of the population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7525 bacteria? I understand how to set it up, but I am not getting any of the optional answers as my answer. I don't know how I'd plug it into my calculator.

asked by Confuzzled
  1. lets find the base a first.

    G=4.5=t/(3.3loga(p))
    a=4, given in problem
    3.3 *4.5log4(p)=t
    14.85(log4(7525)=t
    but log4(7525)=log10(7525)/log10(4)
    14.85*log10(7525)/log10(4)=95.61
    t= 95.61 days
    <<Change of base formula
    Logb x = Loga x/Loga b Pick a new base and the formula says it is equal to the log of the number in the new base divided by the log of the old base in the new base. Solution: Change to base 10 and use your calculator.>>

    posted by bobpursley
  2. Thank you!! This helps tremendously!

    posted by Confuzzled

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