upper bound for $e^{ax^2}$

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I want to find a upper bound for $$e^{ax^2}\leqslant \: ?$$ "a" is a constant and $a\geqslant 0$ .
x is a variable.
I prefer to have a polynomial function or power function (like $ x^{k}$)

is there any upper bound for it?

thanks a lot

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There is no upper bound of the type you mentioned.

$e^{ax^2}$ becomes very large compared to a polynomial.