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