Understanding e and e to the power of imaginary number

How did the fee of e come from compound hobby equation. What does the cost of e honestly 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 $e\ast e$ ,${e}^{3}$ means $e\ast e\ast e$ But what exactly ${e}^{ix}$ mean

I want to know how to visualise ${e}^{i\pi}=-1$ in graphs

How did the fee of e come from compound hobby equation. What does the cost of e honestly 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 $e\ast e$ ,${e}^{3}$ means $e\ast e\ast e$ But what exactly ${e}^{ix}$ mean

I want to know how to visualise ${e}^{i\pi}=-1$ in graphs