why do all signals damp exponentially in nature?

Answer 1

Take the case of a capacitor discharging through a resistor. The current flow depends on the voltage, however when the current flows, the voltage drops as the capacitor discharges, this causes the current to drop and thus the capacitor discharges slower.
This results in a capacitor that never completely discharges. It can be shown mathematically that the discharge curve is an exponentional one.

Inductors/resistors, radioactive decay also follow this model.

Answer 2

A mathematical model of every signal can be constructed from the physical laws which define how it is generated. Solving the model predicts the behaviour of the signal.

For most signals, the physical laws lead to a "second-order differential equation" as the model. Most second-order differential equations have an exponentially-damped solution.

Other differential equations would have other solutions, but they would arise from unusual physical laws. There is just something fundamentally second-order about the laws of mechanics and electromagnetism.

Answer 3

It's based in differential equations, having to do with the fact that the rate of change is based on the current value.