*World of Mathematics*. ©2005-2006 Thomson Gale, a part of the Thomson Corporation. All rights reserved.

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## Exponential Functions

Exponential **functions** have the form f(x)= ab^{x}where a is a non-zero real number, b is a positive real number not equal to 1, and x can take on all real number values. Examples of exponential functions include f(x) = 2^{x}, g(x) = 3(0.5)^{x}, and h(t) = 1300(1.02)^{t}. In general, the graph of f(x) = ab^{x} has a y-intercept at (0,a) and is asymptotic to the x-axis from above if a is positive and from below if a is negative. If b is greater than 1, then the graph is asymptotic to the x-axis as x decreases without bound and increases without bound as x increases without bound. If b is less than 1, then the graph is asymptotic to the x-axis as x increases without bound and increases without bound as x decreases without bound.

Exponential functions have a wide range of applications in finance...

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