Question 179442
Rate of growth answers the question:
"How fast is it getting larger?
It's the same as
"How fast is the child growing?
Growth is a change all by itself,
but I can ask:
"Is that child growing faster than
that other child?
Here's how I would compare the 2 functions:
{{{x^3}}}
---------
x -- f(x) --  change in f(x)
0 -- 0
1 -- 1 -- 1
2 -- 8 -- 7
3 -- 27 -- 19
4 -- 64 -- 37
5 -- 125 -- 61
---------
{{{3^x}}}
x -- f(x) -- change in f(x)
0 -- 1 
1 -- 3 -- 2
2 -- 9 -- 6
3 -- 27 -- 21
4 -- 81 -- 54
5 -- 243 -- 162
---------
The change in {{{f(x)}}} is bigger for
{{{3^x}}} for every term after
{{{f(2)}}}  
So, {{{3^x}}} grows faster