A sample of 2600 bacteria selected from this population reached the size of 2817 bacteria in two hours. How do you find the continuous growth rate per hour?

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Answer 1 · 2015-10-17T22:42:18

Each hour, the population increases by a factor of #sqrt(2817/2600) ~~ 1.0409#, that is an increase of #4.09%#

If #r# is the factor by which the population grows each hour, then starting with a population #P_0#, the population after #t# hours will be:

#P(t) = P_0 r^t#

In our case #P_0 = 2600#, #t = 2# and #P(2) = 2817#.

So

#2817 = 2600 r^2#

Hence #r^2 = 2817/2600#

So #r = sqrt(2817/2600) ~~ 1.0409#

To express this as a percentage, subtract #1# and multiply by #100# to get #4.09%#