SOLUTION: 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 se

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.
Answer by amoresroy(361) (Show Source): You can put this solution on YOUR website!
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.

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