Exploring exponential graphs and the slope of tangents

This applet allows different exponential graphs to be displayed by adjusting the slider. The slope of the tangent at a point is also displayed and the point can be moved along the curve. The graph of e^x can also be displayed along with a tangent and slope for comparison.
By moving the slider can you find what is the value of e? Examining the graph of e^x, does the slope of the tangent show any relationship with the point where it meets the curve?