Chapter 4.1, Problem 45E

45–46 ■ Comparing Exponential and Power Functions In these exercises we use a graphing calculator to compare the rates of growth of the graphs of a power function and an exponential function.

(a) Compare the rates of growth of the functions $f\left(x\right)=2^x\text{ and }g\left(x\right)=x^5$ by drawing the graphs of both functions in the following viewing rectangles.

(i) $\left[0,5\right]\text{ by }\left[0,20\right]$

(ii) $\left[0,25\right]\text{ by }\left[0,{10}^7\right]$

(iii) $\left[0,50\right]\text{ by }\left[0,{10}^8\right]$

(b) Find the solutions of the equation $2^x=x^5$, rounded to one decimal place.