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Bacterial growth

Many bacteria divide in two by binary fission. If division happens at a fixed interval and none die, the number doubles each time. The number of divisions is the time divided by the time between divisions. The population is then the starting number times two to the power of the number of divisions. In the body the immune system usually stops this growth. Phagocytes engulf invaders, and the adaptive defence with B cells and T cells is more precise. Without that brake a small infection would grow very fast.

N = N_0 \cdot 2^{t/d}

growth without death

Symbols

$d$	time between divisions	min
$t$	total time	min
$N_0$	starting number

Example

One bacterium divides every 20 minutes. After 3 hours, that is 180 minutes:

$180/20 = 9$ divisions, and $2^{9} = 512$ bacteria.

Use the same unit of time. Three hours is 180 minutes, not 3.

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