Lesson 5.1: Exponential Growth and Decay

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Lesson 5.1 Exponential Growth and Decay
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General Form of an Exponential Function
The initial amount
The number of periods
y abx
The total amount after x periods
The growth/decay factor
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• When bgt1
• The growth factor b 1 (turn the decimal into
  a )
• When 0ltblt1
• The decay factor 1 b (turn the decimal into
  a )

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Example 1

• The United States population since 1960 can be
  modeled by the function y 180(1.011)x, where x
  is the number of years since 1960 and y is the
  populatio in millions.
• x represents_______________________
• y represents_______________________
• What is the growth factor?
• What is the percentage rate of growth per year?
• What was the population of the United States in
  1960?
• What was the population during the year you were
  born? 2010?

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Example 2

• As technology advances, the price of many
  technological devices such as scientific
  calculators and camcorders goes down. Suppose y
  89(0.94)x represents the cost of a certain
  calculator since 2005.
• x represents________________________
• y represents________________________
• What is the decay factor?
• What is the percentage rate of decay per year?
• What was the cost of the calculator in 2005?
  What would the cost be today?

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Example 6

• The presence of medicine for reducing high blood
  pressure decreases at the rate of 29 per hour in
  a patients bloodstream. This medicine is
  effective until the amount in the bloodstream
  drops below 1.2mg. How long will a dose of 75mg
  be effective?