Exponential Decay
Exponential decay is the decrease in a quantity  according to the law

(1)

for a parameter  and constant  (known as the decay constant), where  is the exponential function and is the initial value. Exponential decay is common in physical processes such as radioactive decay, cooling in a draft (i.e., by forced convection), and so on. Exponential decay is described by the first-order ordinary differential equation

(2)

which can be rearranged to

(3)

Integrating both sides then gives

(4)

and exponentiating both sides yields the functional form (1).