8.2 Properties of Exponential Functions Review: what is an

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8.2 Properties of Exponential Functions
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Review what is an asymptote?
Walking halfway to the wall
An Asymptote is a line that a graph approaches as
x or y increases in absolute value.
In this example, the asymptote is the x axis.
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Graphing yabx when alt0

• Ex Graph

Sketch your prediction of what the graph will
look like
Where is the asymptote?
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Translating yabx

• How does the equation change if we want to move
  both graphs up 4 units? Predictions?

Question where is the asymptote now?
To move the graph up or down, add or subtract
units at the end of the equations. No need to use
inverses if you want to go up, add if you want
to go down, subtract.
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Translating yabx

• How does the equation change if we want to move
  both graphs left 4 units? Predictions?

To move the graph left or right, add or subtract
units to the exponent of the equation. Reminder
use the inverse of how you want the graph to move
(e.g. x-4 will move to the right x4 will move
to the left)
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Lets try some

• Graph each function as a translation of y9(3)x

Make a table of values for each Graph, from -3 to
3
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y 9(3)x1
y 9(3)x-4-1
y 9(3)x-4
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e 2.718
What is base e ? e is an irrational number,
approximately equal to 2.718.
Exponential functions with a base of e are useful
for describing continuous growth or decay. In the
graph below, y e is the asymptote to the graph.
y e
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Graphing ex

• Using your graphing calculators, graph yex.
  Evaluate e4 to four decimal places.

We now need to evaluate where x4
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• 2. Press 2nd, Calc and select 1 (value). Press
  enter

3. We are evaluating when x4. Enter 4 for x and
press enter.
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• The value of e4 is about 54.59815

Your turn evaluate e-3
0.0498
So, what is e good for???
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Continuously Compounding Interest

• A Pert

A amount of money in the account P principal
(how much is deposited) r annual rate of
interest t time (in years)
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Example Continuously Compounded Interest Problem

• You invest 1,050 at an annual interest rate of
  5.5, compounded continuously. How much will you
  have in the account after 5 years?

• Start with
• A Pert
• 1050(e)0.055(5)
• 1050(e)0.275
• 1050(1.316531)
• A 1382.36

P1050, r5.5 0.055, t5
Substitute in for p, r, and t Simplify they
power Evaluate e0.275 with your
calculator Simplify
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Lets try one

• Suppose you invest 1,300 at an annual interest
  rate of 4.3, compounded continuously. How much
  will you have in the account after three years?

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Suppose you invest 1,300 at an annual interest
rate of 4.3, compounded continuously. How much
will you have in the account after three years?