Definition:Exponential Order/Real Index

Definition
Let $f\left({t}\right): \R \to \R$ or $\R \to \C$ be a function.

Let $\left \vert \, \cdot \, \right \vert$ be the absolute value if $f$ is real-valued, or the modulus if $f$ is complex-valued.

Let $e^{at}$ be the exponential, where $a \in \R$ is constant.

Then $f\left({t}\right)$ is said to be of exponential order $a$ iff there exists real strictly positive constants $K,M$ such that:


 * $\forall t \ge M: \left\vert {f\left({t}\right)} \right \vert < Ke^{at}$