Question 373067
suppose a population of bacteria in a petri dish has a doubling time of 7.5 hours, how long will it take for an initial population of 11500 bacteria to reach 32000? Round to the second decimal point.

Let t = the number of hours it take for an initial population of 11500     
        bacteria to reach 32000

11,500*2^(t/7.5) = 32,000
       2^(t/7.5) = 32,000/11,500
       2^(t/7.5) = 2.7826
Log both sides
   Log 2^(t/7.5) = Log 2.7826
    (t/7.5)Log 2 = 0.44445
         (t/7.5) = 0.44445/0.3010
              t  = 11.07

It will take 11.07 hours for an initial population of 11500 bacteria to reach 32000.