Which Number is Larger?!

Here is a great question to test your understanding of basic freshman level calculus. The quesitions is:

Which number is larger? e^\pi or \pi^e?


Here, e^\pi means the number e raised to the power pi (hopefully someday I'll learn a way to make this look better... for now you'll just have to bear with me). If you get stuck, here is a file of hints. At the end of the file, you will find two solutions to this problem. If you come up with another solution, give yourself a pat on the back and then let me know. I'd love to add it to the list!