\begin{definition}[Definition:Exponential Order/Real Index]
Let $f: \R \to \mathbb F$ be a function, where $\mathbb F \in \set {\R, \C}$.
Let $f$ be continuous on the real interval $\hointr 0 \to$, except possibly for some finite number of discontinuities of the first kind in every finite subinterval of $\hointr 0 \to$.
{{explain|Establish whether it is "finite subinterval" that is needed here, or what we have already defined as "Definition:Finite Subdivision". Also work out whether we can replace all the above with a link to Definition:Piecewise Continuous Function with One-Sided Limits .}}
Let  $\size {\, \cdot \,}$ be the absolute value if $f$ is real-valued, or the modulus if $f$ is complex-valued.
Let $e^{a t}$ be the exponential function, where $a \in \R$ is constant.
Then $\map f t$ is said to be of '''exponential order''' $a$, denoted $f \in \EE_a$, {{iff}} there exist strictly positive real numbers $M, K$ such that:
:$\forall t \ge M: \size {\map f t} < K e^{a t}$
\end{definition}