Exponential function
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.