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).
