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Warm up. 23. What is the tenth term of a n = 2n + 3? What is the fourth term of a n = 3(2 n ) + 1? 3. Find the 40 th term following sequence 2 , 8, 14, 20,.. 4. Find the 6 th term following sequence - 80, 40,-20,. 49. 236. 5/2. Review HW. Average Rate of Change. - PowerPoint PPT Presentation
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Warm up1. What is the tenth term of an = 2n + 3?
2. What is the fourth term of an = 3(2n) + 1?
3. Find the 40th term following sequence 2, 8, 14, 20,..
4. Find the 6th term following sequence -80, 40,-20,..
23
49
236
5/2
Review HW
Average Average Rate of Rate of ChangeChange
Rate of ChangeRate of Change
•Ratio describing how one quantity changes as another quantity changes
•Slope can be used to describe it
Rate of ChangeRate of Change
•Positive – increases over time
•Negative – decreases over time
Rate of ChangeRate of Change
•Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time
Rate of ChangeRate of Change
•Horizontal lines have 0 rate of change
•Vertical lines have undefined rate of change
Average Rate of ChangeAverage Rate of Change
2 1
2
2
1
1
2 1
( ) ( )y ym becomes
x x
f x f x
x x
Ex 1 Find the Average Rate of Change
f(x) = 2x2 – 3 from [2, 4].
2 1
2 1
( ) ( ) (4) (2)
4 2
f x f x f f
x x
29 5
4 2
1
24
22
Ex 2 Find the Average Rate of Change
f(x) = 3x – 2 from [2, 5].
2 1
2 1
( ) ( ) (5) (2)
5 2
f x f x f f
x x
241 7
3
234
783
f(x) = -4x + 10 from [-1, 3].
m = -4
Ex 3 Find the Average Rate of Change
A. Find the rate of change from day 1 to 2.
m = 11
Ex 4 Find the Average Rate of Change
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.
9130.3
3
In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011.
m = -5
Ex 5 Find the Average Rate of Change
Year (x) Households in Millions f(x)
2008 66
2009 61
2010 56
2011 51
51 66
2011 2008
What does this mean?It decreased 5 million households per year from 2008 – 11.
Class WorkClass WorkWalking Task
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.
The Data
Time (seconds) 0 1 2 3 4 5 6 7 8 9 10
Dwain’s position (feet) 0 4 8 12 16 2
0 24 28 32 36 40
Beth’s position (feet) 0 1 3 6 10 15 20 25 30 3
5 40
Draw a graph. Should you connect the
dots?
Beth (blue)Dwain (Purple)
Describe how Dwain and Beth should walk in order to match their data.
Beth (blue)Dwain (Purple)
What is Beth and Dwain’s average speed from 1 to 2 seconds?
HomeworkHomework
Rate of Change18 problems
