Warm up What is the tenth term of an = 2n + 3? What is the fourth term of an = 3(2n) + 1? If bn = bn-1  4 and b3 = 16, what is b5? If an = an-1 + 7 and a1 = 10, what is a4?

Review HW

Average Rate of Change

Coordinate Algebra UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems? Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5 Today’s Question: What is rate of change? Why would you need to find the rate of change? Standards: F.IF 6

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

Rate of Change Positive – increases over time Negative – decreases over time

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

Rate of Change Horizontal lines have 0 rate of change Vertical lines have undefined rate of change

Average Rate of Change

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

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

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

A. Find the rate of change from day 1 to 2. Ex 4 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. 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.

Ex 5 Find the Average Rate of Change Households in Millions f(x) In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. 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.

Class Work Walking 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.

Should you connect the dots? The Data Time (seconds) 1 2 3 4 5 6 7 8 9 10 Dwain’s position (feet) 12 16 20 24 28 32 36 40 Beth’s position (feet) 15 25 30 35 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?

Rate of Change 18 problems Homework Rate of Change 18 problems