Among all exponential functions of the form [math]f\left(x\right)=a^x[/math], one of them has a particularly nice property. When the base of the exponent, [math]a[/math], is approximately 2.71828, the line tangent to the graph of [math]f[/math] at [math]x=0[/math] has slope 1. Use the interactive figure below to confirm this. (You can use the arrow keys on your keyboard for fine adjustment of the slider.)[br][br]The exact value for [math]a[/math] that produces a tangent line of slope 1 is the famous number [math]e[/math]. In fact, this is one way that [math]e[/math] can be [i]defined[/i].