It is easily verified that the graphs of y = x² and y = e^x have no points of intersection (for x > 0), and the graphs of y = x³ and y = e^x have two points of intersection. It follows that for some real number 2 < p < 3, the graphs of y = x^p and y = e^x have exactly one point of intersection (for x > 0). Using analytical and/or graphical methods, determine p and the coordinates of the single point of intersection.