What is e (2.718…) and why does it literally appear everywhere?

Question

What is e (2.718…) and why does it literally appear everywhere?

In: 756

Answer 1

It’s less useful to think of the number e than the function f(x)=e^x. This is the unique function whose slope is always equal to its value. The constant e is just this function evaluated at x=1.

This function is important because a lot of things grow at a rate proportional to their current value, because each thing is producing more of the thing (think population of some animal).