April 26, 2016
Section 3.1
Exponential and Logistic Functions
f (0) = a
(b > 1)
Consider the graph of
a=1
b=e
Domain: (−∞, ∞)
Range: (0, ∞)
0
[-6.6, 6.6] [-2.1, 6.1]
∞
What is the y-intercept? (0, 1).
What asymptote does the graph have? y = 0
Does the graph exhibit any symmetry? No
Is the graph continuous? Yes on (−∞, ∞).
Is the graph increasing or decreasing?
It is increasing on (−∞, ∞).
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April 26, 2016
(0 < b < 1)
Consider the graph of
Domain: (−∞, ∞)
Range: (0, ∞)
∞
[-6.6, 6.6] [-2.1, 6.1]
0
What is the y-intercept? (0, 1).
What asymptote does the graph have? y = 0
Does the graph exhibit any symmetry? No
Is the graph continuous? Yes on (−∞, ∞).
Is the graph increasing or decreasing?
It is decreasing on (−∞, ∞).
How does this differ from the previous graph?
The difference is that this graph is decreasing
instead of increasing. The graph is reflected
over the y-axis.
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April 26, 2016
What happens if b < 0? Graph
using the window [-6.6, 6.6]; [-4.1, 4.1].
If the function is an exponential function, state the base
and initial value. For those that are not, tell what kind of
function it is.
This is a monomial function.
The base is 3; the initial value is 1.
This is a power function.
This is a constant function.
The base is e; the initial value is 5.
This is a power tower function.
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April 26, 2016
Compute the exact valuer of the function for the given
x-value without using a calculator.
(a)
(a)
(b)
(c)
(d)
(e)
(f)
(d)
(c)
(e)
(b)
(f)
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April 26, 2016
Find an exponential function whose graph
passes through the points (0, 12) and (2, 108).
A useful fact especially for Calculus students.
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April 26, 2016
Page 263 #58
The amount C in grams of carbon-14 present
in a certain substance after t years is given by
a) What was the initial amount of carbon-14
present?
C(0) = 20
b) How much is left after 10,400 years?
About 5.65 grams of carbon-14 remain.
c)When will the amount left be 10g?
There will be 10 grams of C-14 remaining in
about 5700 years.
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