Listeria monocytogenes is a bacteria that rarely causes food poisoning. At a temperature of 10 °C, it takes about 7 h for the bacteria to double. If the bacteria count in a sample of food is 100, how long will it be until the count exceeds 1 000 000?
So the doubling time is 7 hours, and we have:
number = 100(2)^(t/7) where t is the number of hours
100(2)^(t/7) > 1,000,000
2^(t/7) > 10,000 , assume they are equal
take log of both sides
(t/7) log 2 = log 10,000
(t/7) = 4/log2 = 13.2877..
t = 93.014 hours