In Advanced Engineering Mathematics, a function $f$ is said to be of exponential order if there exist constants $c, M>0,$ and $T>0$ such that $|f(t)| \leq Me^{ct}$ for all $t>T.$
However, later, it said $t^{-2/3}$ is not an exponential order because $t^{-2/3}$ is unbounded near $t=0.$
I think the unbounded issue near $t=0$ is not related to the matter of exponential order.
Are there more conditions for a function to be in an exponential order?