Exponentially

I hear the term “exponentially” being misused sometimes as it related to growth. Exponential growth label is appropiate if the growth in question depends on the current size of a certain population. For example human population growth “depends” on current size, more people will have more children, for the simple fact that people themselves partaking in the act of increasing the population (if you know what I’m sayin’).

Mathematically the simplest version is dy/dt = \alphay, see the growth rate at time t is proportional to y, the current size y. The solution of this linear differential equation is in the form of y = Ae^{\alpha*t} the ^ sign means “power of”. The “e” sign, e^x, is called the “exponential function”, that’s where the words “growing exponentially” comes from.

So if there is growth, but the growth rate at time t does not depend on the current size, dont say “grows exponentially”.. The correct term is… “there will be more”.