SOLUTION: Hello dear tutor, I need help with a certain math problem today that we just learned in class, but I can only get how to do really with like an actual example from my homework, w

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Question 179442: Hello dear tutor,
I need help with a certain math problem today that we just learned in class, but I can only get how to do really with like an actual example from my homework, which is why I am here, trying to learn! So here is the question! Thanks so much for helping out! it means ALOT!

Which grows faster as x increases, x^3, or 3^x? Explain.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
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 -- f(x) -- change in f(x)
0 -- 0
1 -- 1 -- 1
2 -- 8 -- 7
3 -- 27 -- 19
4 -- 64 -- 37
5 -- 125 -- 61
---------

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 is bigger for
for every term after

So, grows faster