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# Growth rate of an exponential function

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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).

##### Solution Summary

The solution uses the derivative and relative growth rate of an exponential function to answer both questions.

##### Solution Preview

In everyday language, exponential growth means very fast 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 ...

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