Exponential decay is the decrease in a quantity according to the law
(1)
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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)
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which can be rearranged to
(3)
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Integrating both sides then gives
(4)
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and exponentiating both sides yields the functional form (1).