College Algebra, Chapter 5, 5.1, Section 5.1, Problem 48

a.) Compose the rates of growth of the functions $f(x) = 3^x$ and $g(x) = x^4$ by drawing the graphs of both functions in the following viewing rectangle.
$(i) [-4,4] \text{ by } [0,20] \qquad (ii) [0,10] \text{ by } [0,5000] \qquad (iii) [0,20] \text{ by } [0,105]$
b.) Determine the solutions of the equation $3^x = x^4$

a.)
$(i) [-4,4]$ by $[0,20]$



$(ii) [0,10]$ by $[0,5000]$



$(iii) [0,20]$ by $[0,105]$


It shows from the graph that the growth rate of the function $f(x) = 3^x$ is greater than the growth rate of the function
$g(x) = x^4$ as the values of $x$ becomes larger.

b.) Based from the graphs, both functions are equal when $x$ is approximately $1.55$ and $7.30$