Assignment:
In everyday language, exponential growth means very fasy growth. In this problem, you will see that any exponentially growing function eventually grows faster than any power function.
(a) Show that the relative growth rate of the function f(x) = 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 rate of the function g(x) = e^kx is larger than the relative growth rate of f(x).
Provide complete and step by step solution for the question and show calculations and use formulas.