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.

Then:


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

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