Why do capacitors discharge exponentially?

What you experienced is a exponential decay on both the flow of the water and the pressure with which it exits... both analogous to the exponential decay of the current and the voltage of the capacitor. The hole in the bucket represents a fixed resistance to flow analogous to a resistor load that discharges a capacitor. read more

A resistor-capacitor discharge voltage with scale factors is [math]v(t) = V_oe^{-t/RC}[/math]. This “rate of change is proportional to the amount of stuff” idea applies to lots of natural processes. read more

If the capacitor is charged from a constant voltage source, it will be charged exponentially as you say. If the capacitor is charged from a constant current source, it will be charged linearly (as in your recent thread). The current source will have to work harder and harder to keep its current constant though. read more

It is exponential decay. If we discharge a capacitor, we find that the charge decreases by half every fixed time interval - just like the radionuclides activity halves every half life. If it takes time t for the charge to decay to 50 % of its original level, we find that the charge after another t seconds is 25 % of the original (50 % of 50 %). read more