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5.2 Exponential Functions
and Graphs
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Graphing Calculator Exploration
Graph in your calculator and sketch in your notebook:
a)
b)
c)
d)
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Exponential Growth: b>1
• b≠1, b>0
• Increasing
• Asymptote: y=0
• Domain: (-∞,∞)
• Range: (0,+∞)
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Exponential Decay: 0<b<1
• b≠1, b>0
• Decreasing
• Asymptote: y=0
• Domain: (-∞,∞)
• Range: (0,∞)
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Exponential Functions
What happens when a < 0?
Given the function:
The graphs are reflected about the x-axis
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Graphing Calculator Exploration
Graph in your calculator, sketch in your notebook and make a table of the ordered pairs for -2 ≤ x ≤ 2.
e)
f)
g)
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Exponential Functions
When a>1, the graph of y = bx vertically stretches
When 0>a>1, the graph of y = bx vertically shrinks
Given the function:
How does the value of a affect the graph of y = bx ?
“multiply y’s by a”
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y = a•b x–h + k
How do h and k affect the graph of
y = a•bx ?
h causes y = a•bx to shift horizontally h units right if h > 0 or left if h < 0
k causes y = a•bx to shift vertically k units up if k > 0 or down if k < 0
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Practice
Graph. Use integer values of x from -2 to 2 in your table. Describe how the graph can be obtained from the graph of the basic exponential function.
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Compound Interest
A = the amount of money that you have after a certain number of years
P = the principal (initial quantity of money)
r = percentage rate (change to a decimal)
t = time in years
n = number of times compounded per year
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Practice
5) You deposit $5000 into an account, which earns 6% compound interest. Assuming that you do not withdraw any money from the account, after 4 years, how much money will you have…a) if the account is compounded monthly?
b) if the account is compounded quarterly?
c) if the account is compounded daily?
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Let’s say that:r=100%P=1t=1
Compound Interest
That yields:
What happens to A as n∞ ?
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Natural base, e - the Euler #
Use the e button on your calculator to find e1.35 to four decimal places.
Graph: y = ex
Graph: y = e−x
e ≈ 2.718281828