e-folding time

A quantity's e-folding time is the time over which it grows or shrinks by a factor of e (2.171828.., Euler's number), quantifying exponential growth or shrinkage. The term is more commonly used for growth; for shrinking quantities, other terms are used, including relaxation time and mean lifetime, and within some areas of science and engineering, it is what is generally meant by lifetime (e.g., the phrase radiative lifetime). The term half-life is analogous to relaxation time but is the time for shrinkage by a factor of 2. The term doubling time is analogous, for growth by a factor of 2. There is a fixed ratio between these based on a factor of 2 versus those based on a factor of e. Equivalences:

The irrational number, e, is used because it offers some advantageous mathematical relationships. Among these is that relaxation time (based on e) of some type of decaying particles (e.g., free neutrons) does indeed equal the mean of their lifetimes.