Without the tools of calculus, you just have to play with it.
\(\displaystyle x^{100}\) This is big for relatively small x > 0.
\(\displaystyle e^{x}\) This gets really big, too. I wonder which one outpaces the other.
Note: Don't forget to look out past x = 100 before you make up your mind.
It is one of the purposes of calculus to give you an idea how to deal with such problems more easily. It would be good to have some idea about this one before you get there. Computer programmers know the difference between polynomial time and exponential time. There is a rule of thumb.
As was stated before, a placement test is intended to place you where it seems appropriate. If you magically get things right, things you don't actually know about, will that be telling the truth to the placement test?