10.1 Exponential Function

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10.1 Exponential Function

• Exponential Growth and Decay

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Remember the Rules of Exponents

• When you are multiplying like Bases, you add the
  exponents.
• When you are taking an exponent to a power, you
  multiply the exponents.

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The power of Exponential functions

• A Famous example of Exponential Growth
• An employer tells you he will double your pay
  every day for a month, if you work ten hours a
  day.
• Day one you are given a penny.
• Is these a good day for you?

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Lets see what you paid is for the week.

• 0.01 0.02 0.04 0.08 0.16 0.32 0.64
• After seven days of ten hour days
• 1.27 Wow
• Do you want to Quit?

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Lets Say you keep work those long hours

• Lets see what the pay is the next week.

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Lets Say you keep work those long hours

• Lets see what the pay is the next week.

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Lets Say you keep work those long hours

• Lets see what the pay is the next week.

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Lets Say you keep work those long hours

• Lets see what the pay is the next week.

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What is the pay for the month?

• The Grand total.
• Exponential is powerful stuff.
• The equation for this model was
• Every day cash 0.01 2x

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Exponential Function

• y abx
• If a gt 0 and b gt 1,
• then it is a Growth Function
• If a gt 0 and 0 lt b lt 1
• ( in or words a fraction)
• , then it is a Decay Function

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Exponential Function

• What is
• the Range and Domain
• Domain is the x parts
• All Real numbers.
• Range is the y parts
• Greater then Zero

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So how do you plot a Growth function?

• Plug in value for x and solve for y

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So how do you plot a Growth function?

• Plug in value for x and solve for y
• Zoomed in

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So how do you plot a Decay function?

• Plug in value for x and solve for y

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So how do you plot a Decay function?

• Plug in value for x and solve for y
• Zoomed in
• What do you see in both Zoomed in graphs

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So how do you plot a Decay function?

• Plug in value for x and solve for y
• Zoomed in
• What do you see in both Zoomed in graphs
• Both graphs Go through (0,1)

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Growth or Decay Function?

• y (0.7)x
• y ½(3)x
• y 10(1.6)x

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Growth or Decay Function?

• y (0.7)x Decay
• y ½(3)x
• y 10(1.6)x

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Growth or Decay Function?

• y (0.7)x Decay
• y ½(3)x Growth
• y 10(1.6)x

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Growth or Decay Function?

• y (0.7)x Decay
• y ½(3)x Growth
• y 10(1.6)x Growth

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Write the exponential function

• In December of 1990, there were 5,283,000
  cellular telephone subscribers in the United
  States. By December of 2000, this number had
  risen to 109,478,000.
• Use the equations yabx
• a is the starting amount 5,283,000
• How do you find b?

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Finding b

• Write the equation
• new amount old amount (b) exponent
• Exponent 2000 - 1990

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Finding b

• Write the equation
• new amount old amount (b) exponent
• Exponent 2000 - 1990

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Use the Equation to find the amount of Cell Phone
Now

• Find exponent for the year 2012.
• 2012 1990 22

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Here is a something Different

• Solve

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Here is a something Different

• Solve
• If the base are the same, the exponents are
  equal.

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The Bases must be the same.

• Solve

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The Bases must be the same.

• Solve

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The Bases must be the same.

• Solve

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The Bases must be the same.

• Solve

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The Bases must be the same.

• Solve

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Homework

• Page 528
• 21 53 odd
• 57, 58

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Homework

• Page 528
• 22 54 even
• 62 - 64