3.3 rate of change ink.notebook. October 24, page 105. page Rates of Change. page 107. Standards. Lesson Objectives

Transcription

1 3.3 rate of change ink.notebook page 105 page Rates of Change Lesson Objectives Standards page Rates of Change Press the tabs to view details. 1

2 Standards Lesson Notes Lesson Objectives Standards Lesson Notes F.LE.1 F.LE.1 F.LE.1 S.ID.7 S.ID.7 S.ID.7 S.ID.7 I will calculate the slope from 2 points I will calculate the slope from a table I will calculate the slope from a graph I will calculate the rate of change in a word problem I will interpret the rate of change in a word problem I will identify the rate of change from a graph and show that it is growing at a constant rate I will determine the rate of change from a table I will determine from a table if a function is linear I will identify the slope of a graph I will identify the slope from a linear equation I will interpret the rate of change in a word problem I will interpret the y intercept in a word problem. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Press the tabs to view details. Press the tabs to view details. Rate of Change: A ratio that describes, on average, how much one quantity changes with respect to a change in another quantity. The rate of change tells, on average, how a quantity is changing over time. 1. Use the table to find the slope. Then explain its meaning. Ratio of the difference in the dependent variable to the difference in the independent variable. 2

3 3.3 rate of change ink.notebook Refer to the graph at the right. a) Find the rate of change of prices from 2002 to Explain the meaning of the rate of change. b) Without calculating, find a two-year period that had a greater rate of change than Explain. 3

4 3.3 rate of change ink.notebook 5. the car the The average retail price in spring of 2008 for a used is shown in the table at right. Find rate of change in the value of the car from 5 years to 7 years old. Age (years) Value ($) 2 15, , , , , A ladder leaning against a wall has a drop of 24 inches and a run of 6 inches for each step. Find the slope of the ladder. 7. In 1996, there were 171 area codes in the United States. In 2007, there were 215. Find the rate of change from 1996 to

5 On Your Whiteboards Find the rate of change for each graph. Use Labels!!! a) Write the equation of the line from each graph in slope intercept form. b) 8 ft per min 5

6 c) The cost of prints from an online photo processor is given by C(p) = p. $29.99 is the cost of the membership, and p is the number of 4-inch by 6-inch prints. What does the slope represent? a) cost per print b) cost of the membership c) cost of the membership and 1 print d) number of prints d) The graph represents how much the Wright Brothers National Monument charges visitors. How much does the park charge each visitor? On the Worksheet Homework 6

7 Review: Find the slope of the line that passes through each pair of points. 5. Use the table to find the slope. Then explain its meaning. 1. (4, 9) (1, 6) 2. ( 4, 1) ( 2, 5) 3. ( 4, 1) ( 4, 5) 4. (2, 1) (8, 9)

8 10. Last summer a family took a trip to a beach that was about 200 miles away from their home. The graph shows the distance driven, in miles, and the time, in hours, taken for the trip. What was their average speed from hour 1 to hour 4? Miles (4, 150) (1, 50) (6, 200) (5, 150) Hours 11. The graph shows the population growth in China. Find the rates of change for and for The table shows the population density for the state of Texas in various years. Find the average annual rate of change in the population density from 2000 to If a ladder is leaning against a wall so that each step has a drop of 18 inches and a run of 8 inches, what is the slope of the ladder? 14. The SheiKra roller coaster at Busch Gardens in Tampa, Florida, features a 138 foot vertical drop. What is the slope of the coaster track at this part of the ride? 8

9 15. A daily newspaper had 12,125 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five year period? 16. In 2003, 421 quadrillion Btu (British thermal units) of energy were consumed worldwide. It is expected that 563 quadrillion thermal units will be consumed in Which of the following is the expected rate of change in consumption from 2003 to 2015? a) about quadrillion Btu per year b) about quadrillion Btu per year c) about 142 quadrillion Btu per year d) about years per quadrillion Btu Answers: 9