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| A quantity is said to be subject to exponential decay if it
decreases at a rate proportional to its value. Symbolically,
this can be expressed as the following differential equation,
where N is the quantity and λ is a positive number called the
decay constant: The solution to this equation is : Here N(t) is
the quantity at time t, and is the (initital) quantity, at time
t=0. This is the form of the equation that is most commonly used
to describe exponential decay. The constant of integration
denotes the original quantity at . (The notation λ for the decay
constant is a remnant of the usual notation for an eigenvalue.
In this case, λ is the eigenvalue of the opposite of the
differentiation operator with as the corresponding
eigenfunction). Measuring rates of decayEdit If the decaying
quantity is the number of discrete elements of a set, it is
possible to compute the average length of ti