TITLE: e and its applications
QUESTION [8 upvotes]: In math when people want to model population growth or radioactive decay we use exponential functions. In many cases, we use base $e$. My question is, what is the purpose of using base $e$ rather than some other base?

REPLY [2 votes]: The exponential decay phenomena in nature do not involve $e$, but other basis of arbitrary value (more precisely, there are arbitrary time constants). In a way, $e$ does not exist in nature, neither in the discharge of condensers, nor in the decay of radioactive materials, nor on the spirals of sunflowers, nor in the growth of compound loan interests.
$e$ is the preferred base of mathematicians because it is convenient, in the sense that it is the only base for which $$\left(b^x\right)'=b^x.$$
For other bases, a conversion factor appears. This is the very same reason why radians are used to measure angles.
On the opposite, the base $10$ that we use for our numeration system is deeply grounded in human anatomy, and base $2$ is pretty useful in the theory of information and computer science.