complex analysis - Understanding $e$ and $e$ to the power of imaginary number

How did the value of $e$ come from compound interest equation. What does the value of $e$ really mean...

Capacitors and inductors charge and discharge exponentially, radioactive elements decay exponentially and even bacterial growth follows exponential i.e., $(2.71)^x$ ,why can't it be $2^x$ or something.

Also $e^2$ means $e*e$ ,$e^3$ means $e*e*e$
But what exactly $e^{ix}$ mean...

I want to know how to visualise $e^{i \pi} =-1$in graphs... I knw how to get the value of such type of equations but Im not able to understand what they actually mean....
Plz help me...