Compare the rates of growth of the function $f(x) = 2^x$ and $g(x) = x^{5}$ by graphing both functions in the following viewing rectangles.

(i) $[0, 5]$ by $[0, 20]$

(ii) $[0, 25]$ by $[0, 10^7]$

(iii) $[0, 50]$ by $[0, 10^8]$

Find the solution(s) with $x \ge 0$ to the equation $2^x = x^{5}$, correct to the nearest tenth.



Note: if there is more than one solution, give them as a comma separated list (e.g., 5.1, 2.7, 11.4). If there are no solutions, enter None .

Which function is higher to the right of the right-most intersection point?

A. $f(x)$
B. $g(x)$


Which function is higher between the intersection points?

A. $f(x)$
B. $g(x)$
C. Neither
D. Both