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

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 $n t$ minutes it will grow ${2}^{n}$ times.

Hence in the instant case

$\frac{700}{320} = {2}^{\frac{52}{t}}$ or $21.875 = {2}^{\frac{52}{t}}$

or ${\log}_{2} \left(2.1875\right) = \frac{52}{t}$ or $\frac{\log 2.1875}{\log} 2 = \frac{52}{t}$

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

$t = 52 \cdot \frac{0.30103}{0.33995} = 46.05$ minutea

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