Choice A is the correct answer. Exponential always beats polynomial long-term.

1. Fundamental fact: For any polynomial $x^n$ and any exponential $a^x$ (where $a > 1$), exponential eventually dominates.
2. Comparison: As $x \to \infty$, $e^x$ grows much faster than $100x^2$.
3. Example: At $x=20$, $100(400) = 40,000$ but $e^{20} \approx 485,165,195$.

💡 Strategic Tip: Exponential > Polynomial > Logarithmic (long-term growth rates).

Choice B is incorrect because polynomials grow slower than exponentials. Choice C is incorrect because they have fundamentally different growth rates. Choice D is incorrect because we can definitively determine this.