Exponential Decay

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8.8 Exponential Growth and Decay Cont. 4/23/08

• Exponential Decay
• Modeled with the function y a bx for a gt 0
  and 0 lt b lt 1.
• y a bx
• a the starting amount (when x 0)
• b the base, which is between 0 and 1, is the
  decay factor
• x exponent

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Modeling Exponential Decay

• Since 1980, the number of gallons of whole milk
  each person in the United States drinks each year
  has decreased 4.1 each year. In 1980, each
  person drank an average of 16.5 gallons of whole
  milk per year.
• a. Write an equation to model the gallons of
  whole milk per year.
• Relate y a bx
• Define Let x the number of years since 1980
• Let y the consumption of whole milk,
  in gallons
• Let a 16.5, the initial number of
  gallons in 1980
• Let b the decay factor, which is
  100 - 4.1 95.9 0.959
• Write y 16.5 0.959x

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Modeling Exponential Decay

• b. Use your equation to find the approximate
  cost per day in 2000.
• y 16.5 0.959x
• y 16.5 0.95920
• y 7.1
• The average annual consumption of whole milk in
  2000 was about 7 gal/person.

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More Practice!!!!

• Textbook p. 441 442 2 30 even.
• Homework finish problems in textbook.