What is a function that gives the coordinates (1, 4), (2, 16), (3, 64), (4, 256)?

Question

solomonzelman · Answer

if I give you the pattern, you will write the function, okay ?

anonymous · Answer

Well sure. But can you show me how to come up with functions just by being given points as well?

solomonzelman · Answer

4¹  ,  4² ,  4³ ,   4$\small\color{bgrey}{ \rm   ^4  }$

anonymous · Answer

$$f(x) = 4^{x}$$

anonymous · Answer

You are freaking awesome!!!

anonymous · Answer

Thanks so much @SolomonZelman. But how did you know?

solomonzelman · Answer

Well, I don't want to say that it is common sense, because when I say "common sense" to people they think that I am calling them stupid (even though I am not).. well, but that is what it is, it is common sense, just figured out :)