# Exponential increase

“Increasing exponentially” is a common phrase used by analysts and commentators to describe a certain kind of growth. However, more often than not, this phrase is misused and any fast growth is termed as “exponential”.

If f(x) is a function of x, f(x) is said to be exponential if and only if it can be written in the form:

$f(x) = K alpha ^x$

So if your growth is quick but linear, then it is not exponential. While on the topic, I want to point you to two posts I’ve written on my public policy blog for Takshashila: one on exponential growth in bank transfers that I wrote earlier today and another on exponential growth in toilet ownership. The former shows you how to detect exponential growth and in the latter I use what I think is an innovative model to model toilet growth as exponential.