a person can also look at the picture to see why the number "e" is important for exponential functions. the picture has three different curves. the curve with the black points is an exponential function with a base slightly smaller than "e". the curve with the short black lines is an exponential function with a base slightly bigger than "e". the blue curve is an exponential function with a base exactly equal to "e". the red line is a tangent to the blue curve. it touches the blue curve at one point without crossing it. a person can see that the red curve crosses the "x"-axis, the line that goes from left to right at -1. this is true only for the blue curve. this is the reason that the exponential function with the base "e" is special.