A sample of 2100 bacteria selected from this population reached the size of 2169 bacteria in one and a half hours. How do you find the hourly growth rate parameter?

1 Answer
May 12, 2017

Hourly growth parameter is #2.155%# per hour.

Explanation:

An hourly growth parameter of #h#, indicates that in an hour #x# number of bacteria become #xe^h# and in #n# hours it would be #xe^(nh)#

As such in one and a half hour, #2100# becomes #2100xxe^(1.5h)#

Hence #2100xxe^(1.5h)=2169#

i.e. #e^(1.5h)=2169/2100=1.023857#

and #1.5h=ln1.023857=0.0323287488#

and #h=0.0323287488xx2/3=0.02155# or say #2.155%#

Another way which is also used could be as given below.

An hourly growth parameter of #h#, indicates that in an hour #x# number of bacteria become #x(1+h/100)#

and in #n#c hours they become #x(1+h/100)^n#

as in sample #2100# bacteria reach the size of #2169# in one and a half hour, we have

#2169=2100(1+h/100)(1+h/200)#

or #(1+h/100)(1+h/200)=2169/2100=723/700#

This leads to #h=2.179# - (up to #3# decimal places using Goal seek in MSExcel)

Hence, hourly growth parameter is #2.179%# per hour.