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Robert Call
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Exponentials and Logs - Example 4

In mathematics, the exponential function is the function ex, where "e" is the base of natural logarithms. It is a special case of the natural logarithm, which is the inverse function of the exponential function. The exponential function is defined for real arguments x by the power series: The exponential function is a periodic function with period 2. The exponential function is an entire function, which means that it is differentiable for all x and its derivative is nonzero for all x. The exponential function maps the real numbers onto the non-negative real numbers. The exponential function is a special case of the hyperbolic cosine function. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same change in the dependent variable. The graph of y = ex is upward-sloping, and increases faster as x gets larger. Its slope is positive, since ex has a positive slope. The exponential function is also used to model exponential growth, in which a constant change in time gives the same proportional change in some other quantity. The graph of y = ex is upward-sloping, and increases faster as x gets larger. Its slope is positive, since ex has a positive slope. The exponential function is also used to model exponential growth, in which a constant change in time gives the same proportional change in some other quantity.

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RC
Robert Call
University of North Carolina at Chapel Hill
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