exponential function

A function that multiplies by the same fixed factor every time its input goes up by one.

An exponential function has the form $f(x)=b^x$ for a fixed base $b>0$ , $b\neq1$ . Unlike a polynomial, where $x$ is the base, here $x$ sits in the exponent — every unit increase in $x$ multiplies the output by $b$ again, which is what produces runaway growth ( $b>1$ ) or decay toward zero ( $0<b<1$ ).

Examples

$f(x)=2^x$ doubles every time $x$ increases by 1: $f(0)=1$ , $f(1)=2$ , $f(2)=4$ , $f(3)=8$ .