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Which function grows faster, exponential (like 2^n, n^n, e^n etc) or factorial (n!)? Ps: I just read somewhere, n! grows faster than 2^n.
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Factorial functions do asymptotically grow larger than exponential functions, but it isn't immediately clear when the difference begins. For example, for n=5 and k=10 , the factorial 5!= 120 is still smaller than 10^5=10000 .
No, exponential functions are the fastest growing functions so eventually it will overpower the line. There must be a second intersection point. Exponentials will eventually exceed all other functions as they are the fastest growing functions.
We could think of a function with a parameter as representing a whole family of functions, with one function for each value of the parameter. is also an exponential function. It just grows faster than f(x)=2x since h(x) doubles every time you add only 1/3 to its input x.
n! eventually grows faster than an exponential with a constant base (2^n and e^n), but n^n grows faster than n! since the base grows as n increases.
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n! = n * (n-1) * (n-2) * ...
n^n = n * n * n * ...
Every term after the first one in n^n is larger, so n^n will grow faster.
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