A sample of 2000 bacteria selected from this population reached the size of 2266 bacteria in five hours. How do you find the continuous growth rate per hour?

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Answer 1 · 2016-07-02T08:07:03

Continuous growth rate per hour is #2.53%#

Let the growth rate be #x%# in one hour.

So #2000# will become #2000(1+x/100)#

and in five hours it will become #2000(1+x/100)^5#

Hence #2000(1+x/100)^5=2266#

or #(1+x/100)^5=2266/2000=1.133#

Hence #5log(1+x/100)=0.05423#

or #log(1+x/100)=0.05423/5=0.01085#

Hence #1+x/100=1.0253# or

#x/100=0.0253# and #x=2.53#