3.1 exponential functions
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Exponential Function
An example of transcendental function
Exponential functions are used to model a variety of real world phenomena
Growth of populations
Radioactive decay
Epidemics
Absorption of light as it passes through a medium
Magnitudes of sound and earthquakes
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Exponential Functions
If b > 0 and b ≠ 1, then the exponential function with
base b is the function f defined by
base
exponent
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Properties of
The x-axis is the horizontal asymptote of the graph.
The y-intercept of the graph is 1.
The graph is increasing when b > 1, while the graph is decreasing if 0 < b < 1.
The function is one-to-one.
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General Form
The horizontal asymptote of the graph is y = k.
The graph is above the asymptote if a > 0 while the
graph is below the asymptote if a < 0.
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How to sketch the graph?
1. Find the horizontal asymptote. How?
2. Determine two arbitrary points. What points?
3. Locate the points.
4. Use the asymptote-two-point technique!
. | 0a x x h . | 1b x x h
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