Warm up

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Warm up

1. What is the sixtieth term of an -n 3?
2. What is the fifth term of an 5(2n) - 1?
3. If bn bn-1 ? 3 and b3 27, what is b6?
4. If an an-1 17 and a1 11, what is a5?

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Review HW
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Average Rate of Change
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CCGPS Alg2/25/2013
UNIT QUESTION How do we graph functions, and
what can be done to change the way they
look? Todays Question How do we write the
function to represent a sequence?
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CCGPS Alg2/25/2013
(I.N. p55) MCC9-12.F.IF.6 Calculate and
interpret the average rate of change of a
function (presented symbolically or as a table)
over a specified interval. Estimate the rate of
change from a graph.
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Rate of Change

• Ratio describing how one quantity changes as
  another quantity changes
• Slope can be used to describe it

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Rate of Change

• Positive increases over time
• Negative decreases over time

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Rate of Change

• Linear functions have a constant rate of change,
  meaning values increase or decrease at the SAME
  rate over a period of time

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Rate of Change

• Horizontal lines have 0 rate of change
• Vertical lines have undefined rate of change

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Average Rate of Change
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Ex 1 Find the Average Rate of Change

• f(x) 2x2 3 from 2, 4.

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Ex 2 Find the Average Rate of Change

• f(x) 3x 2 from 2, 5.

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f(x) -4x 10 from -1, 3.
Ex 3 Find the Average Rate of Change
m -4
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A. Find the rate of change from day 1 to 2.
Ex 4 Find the Average Rate of Change
m 11
Days (x) Amount of Bacteria f(x)
1 19
2 30
3 48
4 76
5 121
6 192
B. Find the rate of change from day 2 to 5.
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In 2008, about 66 million U.S. households had
both landline phones cell phones. Find the
rate of change from 2008 2011.
Ex 5 Find the Average Rate of Change
Year (x) Households in Millions f(x)
2008 66
2009 61
2010 56
2011 51
m -5
What does this mean?
It decreased 5 million households per year from
2008 11.
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Class WorkWalking Task
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Walking Task

• To begin a class discussion of speed, Dwain and
  Beth want to stage a walking race down the school
  hallway. After some experimentation with a stop
  watch, and using the fact that the flooring tiles
  measure 1 foot by 1 foot, they decide that the
  distance of the race should be 40 feet and that
  they will need about 10 seconds to go 40 feet at
  a walking pace.
• They decide that the race should end in a tie, so
  that it will be exciting to watch, and finally
  they make a table showing how their positions
  will vary over time. Your job is to help Dwain
  and Beth make sure that they know how they should
  walk in order to match their plans as closely as
  possible.

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The Data
Time (seconds) 0 1 2 3 4 5 6 7 8 9 10
Dwains position (feet) 0 4 8 12 16 20 24 28 32 36 40
Beths position (feet) 0 1 3 6 10 15 20 25 30 35 40
Draw a graph. Should you connect the dots?
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Beth (blue)Dwain (Purple)
Describe how Dwain and Beth should walk in order
to match their data.
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Beth (blue)Dwain (Purple)
What is Beth and Dwains average speed from 1 to
2 seconds?
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Classwork

• Rate of Change
• 18 problems