Question

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

Answer 1

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