Exponential Decay

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Exponential Decay
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Decay Factor

• With decay the b will be less than one.
• But, b must be positive.
• Therefore, in decay, b will be a decimal
  smaller than one.

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To Find The Decay Factor With Percents

• Take the percent that it is decaying.
• Subtract it from 100.
• Move the decimal to the left two places.
• If it is decaying 7
• Subtract 7 from 100 93
• Move the decimal to the left two places 0.93
• 0.93 is the decay factor for something decaying
  7.

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Example 1

• A town with the population of 270,000 loses 2.3
  of its residents every year. What will the
  population be after 20 years?
• Find the decay factor
• Subtract 100 - 2.3 97.7
• Move the decimal to the left two places 0.977
• Write the function

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Example 1

• Enter the function in the y screen.
• Look at the table.
• Scroll down to where x is 20.
• Round to the nearest whole person.
• 169,533 people

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Half Life

• When something is said to have a half life, this
  means that it will lose half of its power in the
  time period.
• Its decay factor would be 0.5 (half).

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Example 2

• To treat some forms of cancer, doctors use
  radioactive iodine. Use the graph on page 373 to
  find how much iodine-131 is left in a patient
  eight days after the patient receives a dose of
  20 mCi (millicuries).
• Go 8 days on the horizontal axis (the line before
  10).
• Go up until you touch the red curve.
• Go to the vertical axis and read the value (10
  mCi).

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Part I

• Identify each function as exponential growth or
  exponential decay
• 1.
• 2.
• 3.
• 4.
• Identify the growth or decay factor in each
  problem above.

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Part III

• Find the percent of decrease for each function.
• 1.
• 2.
• 3.
• 4.

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Part IV

• Use a graphing calculator or make a table fo
  values to graph each function. Label each graph
  as growth or decay.
• 1.
• 2.
• 3.

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