Exponential order
= Exponential order
{title2=$|f(t)|\leq Me^{at}\quad(t\geq T)$}
A <function> has exponential order $a\in\mathbb R$ if some $M>0$ and $T\geq0$ give the displayed bound. Bounded <functions>, including <sine>, have exponential order zero; $e^{-2t}$ has exponential order $-2$. The bound need not use the smallest possible $a$. Together with <piecewise continuity>, it guarantees a <Laplace transform> for $\operatorname{Re}s>a$.