Exponential decay

A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5.

A very similar equation will be seen below, which arises when the base of the exponential is chosen to be 2, rather than e. In that case the scaling time is the "half-life".

For example, polonium-210 has a half-life of 138 days, and a mean lifetime of 200 days.

or, by rearranging (applying the technique called separation of variables),

For a decay by three simultaneous exponential processes the total half-life can be computed as above:

In the pharmacology setting, some ingested substances might be absorbed into the body by a process reasonably modeled as exponential decay, or might be deliberately formulated to have such a release profile.

Exponential decay occurs in a wide variety of situations. Most of these fall into the domain of the natural sciences.