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Warm up

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.

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Warm up

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  1. Warm up 23 • What is the tenth term of an = 2n + 3? • 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,.. 49 236 5/2

  2. Review HW

  3. Average Rate of Change

  4. Rate of Change • Ratio describing how one quantity changes as another quantity changes • Slope can be used to describe it

  5. Rate of Change • Positive – increases over time • Negative – decreases over time

  6. 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

  7. Rate of Change • Horizontal lines have 0 rate of change • Vertical lines have undefined rate of change

  8. Average Rate of Change

  9. Ex 1 Find the Average Rate of Change f(x) = 2x2 – 3 from [2, 4].

  10. Ex 2 Find the Average Rate of Change f(x) = 3x – 2 from [2, 5].

  11. Ex 3 Find the Average Rate of Change f(x) = -4x + 10 from [-1, 3]. m = -4

  12. Ex 4 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. m = 11 B. Find the rate of change from day 2 to 5.

  13. Ex 5 Find the Average Rate of Change In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. m = -5 What does this mean? It decreased 5 million households per year from 2008 – 11.

  14. Class WorkWalking Task

  15. 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.

  16. The Data Draw a graph. Should you connect the dots?

  17. Beth (blue)Dwain (Purple) Describe how Dwain and Beth should walk in order to match their data.

  18. Beth (blue)Dwain (Purple) What is Beth and Dwain’s average speed from 1 to 2 seconds?

  19. Homework Rate of Change 18 problems

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