My professor said exponentials will always have higher time complexity compared to polynomials. My question is, do exponentials also have higher time complexity than factorials?
I plotted a chart in Matlab to check it myself.
When range of x is small, from 1 to 10, I get the following chart,
%Matlab script x = [1 : 10]; y1 = factorial(x); y2 = exp(x); plot(x', [y1',y2']); title("N! vs e^N"); legend("O(n!)", "O(e^n)");
But when I bump the range of x from 1 to 1000, I get the following chart,
x = [1 : 1000];
Here exponential is clearly beating factorial.
So, can I say conclusively that exponentials will always have higher time complexity than both factorials and polynomials?