Predict with Linear Models

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Predict with Linear Models

• EQ
• How do certain characteristics of functions
  relate to their graphs?
• GPS
• MM1A1d

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Vocabulary

• Best-fitting line The line that most closely
  follows a trend in data.
• Linear interpolation Using a line or its
  equation to approximate a value between two known
  values.
• Zero of a function An x-value for which
• f(x) 0 (or y 0).

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Example 1Interpolate using an equation

• Nesting Eagles The table shows the number of
  pairs of nesting Bald Eagles at a national
  wildlife reserve from 1998-2002.
• Make a scatter plot of the data.
• Find an equation that models the number of pairs
  of nesting Bald Eagles as a function of the
  number of years since 1998.
• Approximate the number of nesting eagle pairs in
  1999.

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Example 2Extrapolate using an equation

• Nesting Eagles Look back at Example 1.
• Use the equation from Example 1 to approximate
  the number of nesting Bald Eagle pairs in 2003
  and 2005.
• In 2003 there were actually 31 pairs of nesting
  eagles. In 2005 there were actually 34 pairs.
  Describe the accuracy of the extrapolations made
  in part (a).

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Example 3Find the zero of a function

• Race You can run a 100 meter race at an average
  rate of 4.8 meters per second. The distance d
  you have left to run after t seconds is given by
  the function d -4.8t 100. Find the zero of
  the function to the nearest tenth. Explain what
  the zero means in this situation.

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Guided Practice for Examples1, 2, 3

• Sales The table shows the sales (in thousands of
  dollars) of pet care items at one pet store
  during the period 2001 to 2006.
• Find an equation that models the sales of pet
  care items as a function of the number of years
  since 2001.
• Approximate the sales of pet care items for the
  years 2004 and 2007. Tell whether the
  approximation is an interpolation or an
  extrapolation.
• Which of the approximations from part (b) would
  you expect to be more accurate? Explain.
• Find the zero of the function. Explain what the
  zero means in this situation.

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Joke of the Day

• Where can you find an ocean without water?

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Answer

• On a map?