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MAT 142Lecture Video
Series
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Exponential Functions and Their Inverses
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Objectives• Evaluate a function at a given value.• Match an exponential function to its
graph.
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Functions
• x is the independent variable.•Y is the dependent variable.•fred is the name of the function.
y f red(x) 3x 2
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Evaluate.
y f red(x) 3x 2
y tax(d) .18d
y g(x) 3x 2 2x
f red(4)
tax(50)
g()
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Basic Natural Exponential Function
• a is the initial amount (f(0))•e is a number that is approximately 2.71828 (it is on your calculator)
y f (t) aekt
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Graph each of the following functions.
h(t) e13t
g(t) e4t
f (t) e1t
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h(t) e13t
g(t) e4t
f (t) e1t
red
green
blue
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Graph each of the following functions.
g(t) e 4t
f (t) e4t
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g(t) e 4t
f (t) e4t
green
blue
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Basic Natural Exponential Function
• a is the initial amount (f(0))
• k > 0, function strictly increases
• k < 0, function strictly decreasing
y f (t) aekt
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Graph each of the following functions.
h(t) 14
e3t
g(t) 4e3t
f (t) e3t
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h(t) 14
e3t
g(t) 4e3t
f (t) e3t
red
blue
green
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Inverse of the Natural Exponential Function
t 1k
ln ya
y aekt
Where a, k, and t come from the natural exponential function.
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Write the inverse of the exponential function
g(t) 4e3t
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Write the inverse of the exponential function
h(t) 14
e 7t
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The number of bacteria in a culture is given by the function
where t in measured in hours.
n(t) 900e0.1t
How many bacteria will the culture contain in 5 hours?
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Creator and Producer
Elizabeth Jones
for
The School of Mathematical and Statistical Sciences
atArizona State University
Videographer
Mike Jones
©2010 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University