Laplace Transform of Exponential times Function

Theorem
Let $f \left({t}\right): \R \to \R$ or $\R \to \C$ be a function of exponential order $a$ for some constant $a \in \R$.

Let $\mathcal L \left\{ {f \left({t}\right)}\right\} = F \left({s}\right)$ be the Laplace Transform of $f$.

Let $e^t$ be the exponential function.

Then:


 * $\mathcal L \left\{ {e^{a t} f \left({t}\right)}\right\} = F \left({s - a}\right)$

everywhere that $\mathcal L f$ exists, for $\operatorname{Re} \left({s}\right) > a$