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The amount of time required by a bacterial species to go from 1 bacterium to 100 bacterium will depend on it doubling time. This is the time duration during which a substance doubles up or increases its concentration or quantity to 200% of the original value.
The doubling time of a bacteria will vary depending on a number of factors, including availability of food (termed substrate), presence of predators, type of environmental conditions (favorable or unfavorable), presence of nutrients, rate of growth, etc. Even under favorable conditions, each bacterial species will have its own doubling time. For example, aerobic bacteria generally grow very fast and may have a doubling time of 30 minutes or less. On the other hand, anaerobic bacteria grow very slowly and may have a doubling time of a week or so.
For illustration, assuming a doubling time of 1 hour, 1 bacteria will become 2 in 1 hour, 2 will become 4 in 2 ( = 1+1) hours and so on. Mathematically this will be:
Final amount = 2^n, where n is the number of doubling times.
For a final amount of 100: 100 = 2^n
solving which, we get, n = 6.64 doubling times or 6.64 hours (in this case).
Thus, depending on the doubling time (which will vary from bacteria to bacteria) we can calculate the amount of time required to go from 1 bacterium to 100 bacteria.
Hope this helps.
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