Answer
The two points of intersection occur at $~~x = 1.8~~$ and $~~x = 5~~$
$~~g(x) = 5^x~~$ grows more rapidly when $~~x~~$ is large.
Work Step by Step
When we graph $f(x) = x^5$ and $g(x) = 5^x$ , we can see that there are two points of intersection.
When $x = 1.765$:
$f(x) = (1.765)^5 = 17.1$
$g(x) = 5^{1.765} = 17.1$
When $x = 5$:
$f(x) = (5)^5 = 3125$
$g(x) = 5^5 = 3125$
The two points of intersection occur at $~~x = 1.8~~$ and $~~x = 5~~$
When $x \gt 5,~~$ then $~~g(x) \gt f(x)$
Therefore, $~~g(x) = 5^x~~$ grows more rapidly when $~~x~~$ is large.
