This is the type of decay associated with nuclear decay and capacitor discharge. In nuclear decay, each atom has a set probability of decaying over a given time period. In a capacitor, the rate of flow of current is dependant on the charge on the plates. In both cases, a simple differential equation can be derived:

dx/dt = -kx

This, in English, means that the rate of disappearance of x will depend of the amount of x you have left, with k as a rate constant. We can solve this differential equation by inspection, simply by the thought process:

"What, differentiated, gives minus k times itself?"

The answer is, of course Ae^{-kt}, thus we recieve the equation x=Ae^{-kt} giving us values of x for varying t.

For values of the constants, we can put t=0, ie when the system begins. For the radioactive decay, at t=0, x is equal to however many atoms you begin with, or x_{0}. k is the decay constant, given in s^{-1} (This is frequently written as a lambda). T_{1/2} (the half life of your sample) can be found by the equation T_{1/2}=ln(2)/k.