Which function "dominates?"

x^p or p^x

Question

Which function "dominates?"

x^p or p^x

psymon · Answer

I would assume that dominates basically means which climbs faster. In a race to infinitely high in space, which function wins. 

Now generally we know x to be a variable. We don't know what it is, but we can plug numbers into it and see what our answers our. P, though, we have to assume is a constant, a number which does not change. So assuming P does not change, let's just invent a number. Let's say P is 2

$$x ^{2}$$
$$2^{x}  $$

Now we can make a little more sense of this. As x gets bigger and bigger and bigger, which function wins the race to infinity? Can you kinda see what's going to happen and which function is going to get higher faster?

psymon · Answer

@Loser66 I didnt tell him to put that :/ It was something I was planning on showing him before, but I guess he wanted to try and prevent people from interrupting.

loser66 · Answer

just teasing you, I am sorry if my joke frustrated you.

psymon · Answer

Nah, it didnt, lol. I was more worried about others getting annoyed, not myself xD

anonymous · Answer

So basically 2^x "dominates" because it will eventually be closer to infinity than 2^x? Well that makes sense! Thank you.

P.S. : What did I put down 0=?

psymon · Answer

0 =? 
Not sure what you're asking.

anonymous · Answer

Oh that was a face with a question mark ._.

psymon · Answer

Oh. What do you put down for an answer?

anonymous · Answer

I wrote down that 2^x dominates. But I meant what did I put down to prevent people from interrupting?

psymon · Answer

No, not you, I was being teased about another question. Someone earlier posted a question that specifically asked for me.

anonymous · Answer

Oh okay haha. Either way thanks for the help!

psymon · Answer

Yep, np :3