A bacteria population is initially 320. After 52 minutes, they've grown in number to 700. What is the doubling time for this population?

1 Answer
Feb 19, 2016

Bacteria population's doubling time for this population is #46.05# minutes

Explanation:

Let the doubling time of bacteria population be #t#. This means that after #t# minutes, it will be doubled and after #nt# minutes it will grow #2^n# times.

Hence in the instant case

#700/320=2^(52/t)# or #21.875=2^(52/t)#

or #log_2 (2.1875)=52/t# or #(log 2.1875)/log 2=52/t#

or *0.33995/0.30103=52/t# i.e.

#t=52*0.30103/0.33995=46.05# minutea

Hence bacteria population's doubling time for this population is #46.05# minutes