Constant Function is of Exponential Order Zero

Theorem
Let $f_C: \R \to \mathbb F: t \mapsto C$ be a constant function, where $\mathbb F \in \set {\R, \C}$.

Then $f_C$ is of exponential order $0$.

Proof
The result follows from the definition of exponential order, with $M = 1$, $K = \size C + 1$, and $a = 0$.