Warm up What is the tenth term of an = 2n + 3?

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Warm up What is the tenth term of an = 2n + 3? What is the fourth term of an = 3(2n) + 1?

How do I find the average rate of change of a function? 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: How do I find the average rate of change of a function? Standard: MCC9-12.F.IF.6

Average Rate of Change

Rate of Change of a Linear Relationship rise run Rate of Change = The rate of change of a linear relationship is the steepness of the line.

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The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

Engineers refer to the rate of change of a road as the grade.

They often represent the rate of change as a percentage.

8 100 A grade of 8% would mean for every rise of 8 units there is a run of 100 units. = ___%

The steepness of wheelchair ramps is of great importance for safety. 1 12 Rate of change of wheelchair ramp = If the rise is 1.5 m, what is the run?

Determine the rate of change (pitch) of the roof.

Determine the rate of change of each staircase. 2 3

Determine the rate of change. Which points will you use to determine rise and run? Earnings 4 20 What does this rate of change represent? Number of Hours Worked

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 _______________________________have a _____________ rate of change, meaning values increase or decrease at the SAME rate over a period of time

Rate of Change _______________________________have 0 rate of change _______________________________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].

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. 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 What does this mean?

Rate of Change 18 problems Homework Rate of Change 18 problems