Answer
(a) Please see the graphs and explanations below.
(b) $-0.80, 1.52$ and $7.18$
Work Step by Step
(a) First, we compare the rates of growth of the functions $ f(x)=3^x$
and $g(x)=x^4$ by drawing the graphs of both functions on the same set of axes.
(i) in this small view window, we can found two intersects between the two functions, which give the
two solutions needed in (b) as $(-0.80,0.41)$ and $(1.52,5.29)$. Function $g(x)$ shows a faster rate of growth in this region.
(ii) in this window, another intersection point can be found as $(7.18,2649.89)$, and function $f(x)$ shows a faster
growth rate after around $x=6$.
(iii) in this wide viewing window, $f(x)=3^x$ clearly grows much faster than $g(x)$.
(b) The solutions of the equation $3^x = x^4$ can be found as $-0.80, 1.52$ and $7.18$ as indicated above (rounded to two decimal places).
