If we graph the functions x^{2} and 2^{x}, they intersect in three places: One of the points of intersection has a negative value of x, and two have positive values of x. After those intersections, as x approaches ∞ the graph of 2^{x} will always be on top of the function x^{2}. Here are some values of the two functions. We can see that when x = 2 and x = 4 the functions intersect, and that when x is greater than 4 the function 2^{x} is pulling away from the function x^{2}. It's like a horse race, where the function x^{2} is not having a good day. If we take these values and look at the quotient , here's what happens: We're already down to about 0.098 when x = 10, and we've barely started! When x = 100, we're down to Now that's small. We conclude that
