Question: In everyday language, exponential growth means very fast growth. In this problem, you will see that ay exponentially growing function eventually grows faster that any power function

(a) Show that the relative growth rate of the function \[f\left( x \right)={{x}^{n}}\], for fixed n>0, and for x>0, decreases as x increases

(b) Assume k>0 is fixed. Explain why for large x, the relative growth of the function \(g\left( x \right)={{e}^{kx}}\) is larger than the relative growth rate of \(f\left( x \right)\).