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One way to think about the function e to the t is to ask what properties does it have? Probably the most important one, and from some points of view the defining property, is that it is its own derivative. Together with the added condition that inputting 0 returns 1, itamp;#39;s actually the only function with this property. And you can illustrate what this means with a physical model. If e to the t describes your position on a number line as a function of time, then you start at the number 1, and what this equation is saying is your velocity, the derivative of position, is always equal to that position. The farther away from 0 you are, the faster you move. So even before knowing how to compute e to the t exactly, going from a specific time to a specific position, this ability to associate each position with a velocity paints a very strong intuitive picture of how the function must grow. You know that youamp;#39;ll be accelerating, and at an accelerating rate, with an all-around feel
