# Can anyone explain the logic behind why we used exponantial functions to model bacteria growth?

Aug 20, 2016

Imagine that a given strain of bacteria is perfectly predictable: every hour a given bacterium divides into two bacteria. Then, in a given sample, the population of bacteria will double every hour, on the hour. If we look at how this progresses for a starting population $p$, we get something like this:

$\text{Hour Population}$
$\text{0 } p$
$\text{1 } 2 p$
$\text{2 } 4 p$
$\text{3 } 8 p$
$\text{4 } 16 p$
$\ldots$
$\text{n } {2}^{n} p$

Notice that the population has a geometric growth pattern.

However, actual bacteria do not behave quite so nicely. Within a given population, some may reproduce faster or slower than others. The resulting growth rate tends to be well approximated by an exponential curve, rather than a perfect geometric pattern.