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Will $2^x$ take over $x^{1000}$ ?

I thought that exponential functions had the fastest growth rate, however, graphing it on wolfram alpha made it seem as if the initial behaviors of the two functions implied $2^x$ never overtook $x^{1000}$.

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    If we have learned anything over the past few days, it's that [apparent patterns sometimes fail](http://math.stackexchange.com/q/111440/7850)2012-02-22
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    $2^x$ will certainly, **eventually** surpass $x^{1000}$; the initial behavior is irrelevant. $2^x$ overtakes $x^{1000}$ somewhere around $x\approx 13,750$.2012-02-22
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    You can see that $x=2^{16}$. Since $x>16000$, $2^x>2^{16000}=x^1000$2012-02-22
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    @ThomasAndrews: $x$ cannot have a specific value. One can choose any large enough $x$, and yours is sufficient. If you want multicharacter exponents, put them in brackets: x^{1000} renders as $x^{1000}$ instead of x^1000 which shows as $x^1000$2012-02-22

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