Exponential function : An exponential function is a function of the form $f(x)=c^x$ for some constant $c.$ If the constant equals Euler's number $e$ the exponential function is called natural exponential function. For any polynomial function $p$ and any exponential function $f$ we have $\lim \limits_{x\to\infty}\frac{p(x)}{f(x)}=0,$ in other words any exponential function will ultimately be much bigger than any polynomial function.