7.1.1 Exponential Functions, Growth, and Decay Key Objectives • Write, evaluate, and graph exponential functions to model growth and decay situations. Key Terms • An exponential function has the form y = ab x , where b > 0 and b ≠ 1. • An exponential growth function has the form f ( x ) = ab x , where a > 0 and b > 1. • An exponential decay function has the form f ( x ) = ab x , where a > 0 and 0 < b < 1. Example 1 Graphing Exponential Functions
For an exponential growth function, f ( x ) increases as x increases. For an exponential decay function, f ( x ) decreases as x increases. Graphs of exponential growth and decay functions have an asymptote at the x -axis (i.e., the line y = 0). An asymptote is a line that a graphed function approaches as the value of x gets very large or very small.
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