Fastest Growing Function?

The applet below contains a collection of 6 functions.[br]Each function is color-coded so its graph is the same color as its description & equation listed on the right. [br][br][i]Of all these listed functions, which one will eventually "beat all the others", so to speak, with respect to increasing at the fastest rate? Explain your reasoning. [/i]
Quick (Silent) Demo

Information: Fastest Growing Function?