Exponential Decay is the rate of decay with respect to time. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Exponential decreases start fast and get slower, hence the problem with radioactive waste hanging around for ages. True exponential increases and decreases occur whenever the rate of change of something is proportional to the thing itself. The rate of change of decay is given by
The Exponential Decay Formula
is given by
t is the time taken,
is the initial no of atoms present at time t = 0,
N(t) is the no of atoms present after time t,
$\lambda$ is the decay constant.