Chapter 5.1, Problem 12P

In each of Problems $5$ through $12$, determine whether the given function is of exponential order. If it is, find suitable values for $M,K$ and $a$ in inequality $\left(6\right)$ of Definition $\mathrm{5.1.5.}$

$e^{t^3}$

Definition $\mathrm{5.1.5.}$

A function $f(t)$ is of exponential order (as $t\to +\infty$) if there exist real constant $M\ge 0,K>0,\text{and}a$ such that $\left|f(t)\right|\le K{e}^{at}$, when $t\ge M$.