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

2. 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

3. Average Rate of Change

4. 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.

5. Rates of change are seen everywhere.

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

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

8. They often represent the rate of change as a percentage.

9. 8
100
A grade of 8% would mean for every rise of 8 units there is a run of 100 units.
= ___%

10. 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?

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

12. Determine the rate of change of each staircase.2 3

13. 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

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

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

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

17. Rate of Change _______________________________have 0 rate of change
_______________________________have undefined rate of change

18. Average Rate of Change

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

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

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

22. 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.

23. 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?

24. Rate of Change 18 problems
Homework
Rate of Change
18 problems