## Calculus: Early Transcendentals 8th Edition

The two points of intersection occur at $~~x = 1.8~~$ and $~~x = 5~~$ $~~g(x) = 5^x~~$ grows more rapidly when $~~x~~$ is large.
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.