Which of $e^n$ and $2n^2$ grows faster? How would you prove/disprove that $e^n = O(2n^2)$? It's unclear to me which function grows faster.
Try plotting them. You can also notice that as $n$ increases by one, $e^n$ increases by a multiplicative factor of $e^{n+1}/e^n=e$, while $2n^2$ increases by a multiplicative factor of $\frac{2(n+1)^2}{2n^2} \longrightarrow 1$.