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?

Question

2647 views around the world

You can reuse this answer
Creative Commons License

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#