Question

Explain what exponential decay is

Answer 1

A function in which the dependent variable decreases by the same factor over each unit of time

Answer 2

A quantity X follows an exponential decay (decrease) if it decreases at a rate proportional to its current value. This can be written as

$X(t) = X_0 e^{-at}$

with t being the time (can be continuous or discrete steps), and "a" being a rate of decay (the larger "a" the faster the decay). X0 is an initial (at time 0) value of the quatity X. Exponential decay is seen frequently in nature (radioactivity, chemical reactions) and economics.