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Exponential Functions with Base e - Alamo Colleges District

Exponential Functions with Base e Any positive number can be used as the base for an Exponential function, but some bases are more useful than others. For instance, in computer science applications, the base 2 is convenient. The most important base though is the number denoted by the letter e. The number e is irrational, so we cannot write its exact value; the approximate value to 20 decimal places is e It may seem at first that a base such as 10 is easier to work with, but in certain applications, such as compound interest or population growth , the number e is the best possible base. The Natural Exponential Function: The natural Exponential function is the Exponential function ()xfxe= with base e.

Notice that the formula for population growth is the same as that for continuously compounded interest. In fact, the same principal is at work in both cases: The growth of a population (or an investment) per time period is proportional to the size of the population (or the amount of the investment). By: Crystal Hull

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