Chapter 4.1, Problem 46E

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 $f\left(x\right)=3^x\text{ and }g\left(x\right)=x^4$ by drawing the graphs of both functions in the following viewing rectangles:

(i) $\left[-4,4\right]\text{ by }\left[0,20\right]$

(ii) $\left[0,10\right]\text{ by }\left[0,5000\right]$

(iii) $\left[0,20\right]\text{by}\left[0,{10}^5\right]$

(b) Find the solutions of the equation $3^x=x^4$, rounded to two decimal places.