1 / 31

Supplemental Instruction (S I ) schedule: Wednesdays from 5:00-6:00 pm

Supplemental Instruction (S I ) schedule: Wednesdays from 5:00-6:00 pm Mondays from 6:30-7:30 pm in Room 461 in the Burris Library. The first Supplemental Instruction Session will be tomorrow (August 27). Exit Ticket.

harlan-knowles
Télécharger la présentation

Supplemental Instruction (S I ) schedule: Wednesdays from 5:00-6:00 pm

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Supplemental Instruction (SI) schedule: Wednesdays from 5:00-6:00 pm Mondays from6:30-7:30 pm in Room 461 in the Burris Library. The first Supplemental Instruction Session will be tomorrow (August 27)

  2. Exit Ticket The table shows the enrollment at Kennesaw State University in various years. Assuming the enrollment at KSU increased at a constant rate during each time period, answer each of the following questions about the function K = K(y). Source: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books • 1. Explain the meaning of K(1998) in this setting and give its value. • Estimate the value of K(2000). • What is the average rate of change between 2005 and 2009? • Use your answer to question 3 to estimate the enrollment at KSU in 2008.

  3. Exit Ticket Assuming the enrollment at KSU increased at a constant rate during each time period, answer each of the following questions about the function K = K(y). Source: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books • Explain the meaning of K(1998) in this setting and give its value. • Estimate the value of K(2000). • What is the average rate of change between 2005 and 2009? • Use your answer to question 3 to estimate the enrollment at KSU in 2008. K(1998) means the enrollment at KSU in 1998. It’s value is 12,861 • 14,258 students

  4. Sources: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/documents/pdf/FB1997_1998.pdf http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/

  5. Sources: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/documents/pdf/FB1997_1998.pdf http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/

  6. Exit Ticket Assuming the enrollment at KSU increased at a constant rate during each time period, answer each of the following questions about the function K = K(y). Source: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books • Explain the meaning of K(1998) in this setting and give its value. • Estimate the value of K(2000). • What is the average rate of change between 2005 and 2009? • Use your answer to question 3 to estimate the enrollment at KSU in 2008. K(1998) means the enrollment at KSU in 1998. It’s value is 12,861 • 14,258 students Average rate of change from 2005 to 2009 is approximately 958.25 students per year. KSU enrollment in 2008 was approximately 21,431. 18,556 + 3(958.25)

  7. Sources: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/documents/pdf/FB1997_1998.pdf http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/

  8. Sources: http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/documents/pdf/FB1997_1998.pdf http://vic.kennesaw.edu/EIMWebApps/vic/fact_books/

  9. Practice The table at the right shows the number of murders reported in the United States in the years listed. Assume that the number of murders in the United States rose uniformly from 1962 through 1980. Source: http://www.disastercenter.com/crime/uscrime.htm Answer each of the following questions about the function M = M(y). Show work. • Explain the meaning of M(1975) and give its value. • Estimate the value of M(1968). • What was the average rate of change in the number of murdersfrom 1970 and 1975? • Use your answer to question 3 to estimate the number of murders in the U.S. in 1973.

  10. Practice The table at the right shows the number of murders reported in the United States in the years listed. Assume that the number of murders in the United States rose uniformly from 1962 through 1980. Source: http://www.disastercenter.com/crime/uscrime.htm Answer each of the following questions about the function M = M(y). Show work. • Explain the meaning of M(1975) and give its value. • Estimate the value of M(1968). • What was the average rate of change in the number of murdersfrom 1970 and 1975? • Use your answer to question 3 to estimate the number of murders in the U.S. in 1973. M(1975) = 20,510 M(1975) represents the number of murders in the U.S. in 1975. M(1968)  14,410 The average rate of change from 1970 and 1975 was 546 murders per year. The number of murders in the U.S. in 1973 was approximately 19,418.

  11. Practice The table at the right shows the number of murders reported in the United States in the years listed. Assume that the number of murders in the United States rose uniformly from 1962 through 1980. Answer each of the following questions about the function M = M(y). Show work. • Explain the meaning of M(1975) and give its value. • Estimate the value of M(1968). • What was the average rate of change in the number of murdersfrom 1970 and 1975? • Use your answer to question 3 to estimate the number of murders in the U.S. in 1973. • What was the average rate of change in the number of murders from 1980 and 1985. M(1975) = 20,510 M(1975) represents the number of murders in the U.S. in 1975. M(1968)  14,410 The average rate of change from 1970 and 1975 was 546 murders per year. The number of murders in the U.S. in 1973 was approximately 19,418. The average rate of change from 1980 and 1985 was -812. The average rate of decrease is 812 murders per year.

  12. Answers to even-numbered HW problems 51.2 35.8 89.0 Section 1.2 S-8 20.7 Ex 8 a) A(75) means the temperature of a piece of aluminum 75 minutes after it has been removed from the oven.A(75) = 90.5 b) The average decrease per minute is 5 c) The average decrease per minute is .63 d) The rate of cooling is slowing down as the aluminum cools and its temperature approaches room temperature. e) A(73) = 91.8 f) The temperature of the oven is A(0) = 302. Ex 10 a) b) B(2004) means the number of billions of dollars in new construction in the U.S. in the year 2004. B(2004) = 1,054.8 billion. c) 2002 – 2005 d) 2005

  13. Trends and Limiting Values The limiting value of a function (if there is one) is a number that the function (output) values appear to get closer to as the input values get larger and larger. Here, the limiting value appears to be approximately 84.

  14. Last class we said: Afunction can be represented in several ways, including:  As a formula  As a table  As an arrow diagram  As a set of number pairs • As a graph

  15. Number of Deaths from AIDS in the United States by Year Source: United States Centers for Disease Control and Prevention, HIV/AIDS Surveillance Report, Year-End Edition 1995 Represent the relationship between the year and the number of AIDS deaths by D = D(y), where y = the year, and D = the number of deaths.

  16. Number of Deaths from AIDS in the United States by Year

  17. D(1986) = 12,056 12,056 Number of Deaths from AIDS in the United States by Year 50,000 45,000 40,000 35,000 30,000 D(y) = number of deaths 25,000 20,000 15,000 10,000 5,000 19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000 y = year

  18. Number of Deaths from AIDS in the United States by Year 50,000 45,000 40,000 35,000 30,000 D(y) = number of deaths 25,000 20,000 15,000 10,000 5,000 19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000 y = year

  19. Number of Deaths from AIDS in the United States by Year 50,000 45,000 40,000 35,000 30,000 D(y) = number of deaths 25,000 20,000 15,000 10,000 5,000 19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000 y = year

  20. Number of Deaths from AIDS in the United States by Year 50,000 45,000 40,000 ● 35,000 30,000 D(y) = number of deaths 25,000 20,000 15,000 10,000 5,000 19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000 y = year Questions: 1. Use the graph to estimate the value of D(1991) and explain its meaning. D(1991) means the number of deaths due to AIDS in the U.S. in 1991. From the graph, D(1991) is approximately 36,000.

  21. Number of Deaths from AIDS in the United States by Year 50,000 ● 45,000 40,000 35,000 30,000 D(y) = number of deaths 25,000 20,000 15,000 10,000 5,000 19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000 y = year Questions: 2. In what year did the maximum number of AIDS deaths occur and what was that number? The maximum number of AIDS deaths occurred in 1995 and was approximately 47,500.

  22. Number of Deaths from AIDS in the United States by Year 50,000 45,000 40,000 35,000 30,000 D(y) = number of deaths 25,000 20,000 15,000 10,000 5,000 19 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2000 y = year Questions: 3. During which years were the number of AIDS deaths decreasing? Between what 2 years was the decrease most rapid? The number of AIDS deaths decreased from 1995 to 2000. The most rapid decrease was between 1995 and 1997.

  23. Stock Market Performance The Dow Jones Industrial Average It is an index that shows how 30 large, publicly owned companies based in the United States have traded during a standard trading session in the stock market. 13 12 Dow Jones Average (in thousands of dollars) 11 10 9 2000 2001 2002 2003 2004 2005 2006 2007 2008 y = year Properties of graphs: • Increasing or decreasing • Concavity • Points of Inflection

  24. Stock Market Performance The Dow Jones Industrial Average The function increases from 2000 to 2001, and from 2004 to 2008, 13 12 Dow Jones Average (in thousands of dollars) 11 10 9 2000 2001 2002 2003 2004 2005 2006 2007 2008 y = year Properties of graphs: • Increasing or decreasing The function decreases from 2001 to 2004 and after 2008.

  25. Stock Market Performance The Dow Jones Industrial Average 12,000 11,000 9,200 13 During which years was the Dow Jones increasing more rapidly – from 2000 to 2001 or from 2005 to 2006? 12 Dow Jones Average (in thousands of dollars) 11 10 Change in value: 2000-01 12,000 – 9,000 = $3,000 9 2005-06 11,000 – 9,200 = $1,800 2000 2001 2002 2003 2004 2005 2006 2007 2008 y = year To determine when increase (or decrease) is more rapid over equal time periods, compare the change in value.

  26. Stock Market Performance The Dow Jones Industrial Average 13,300 11,000 Change in value: 2005-06 9,200 2006-08 13 During which years was the Dow Jones increasing more rapidly – from 2005 to 2006 or from 2006 to 2008? 12 Dow Jones Average (in thousands of dollars) 11 10 9 2000 2001 2002 2003 2004 2005 2006 2007 2008 y = year

  27. Stock Market Performance The Dow Jones Industrial Average 13,300 11,000 Average rate of change: 2005-06 9,200 2006-08 13 During which years was the Dow Jones increasing more rapidly – from 2005 to 2006 or from 2006 to 2008? 12 11 10 9 2000 2001 2002 2003 2004 2005 2006 2007 2008 y = year To determine when increase (or decrease) is more rapid regardless of the time interval, compute the average rate of change for each interval. The interval with the larger average rate of change is increasing (or decreasing) more rapidly.

  28. 4.20 4.10 4.00 Price per Gallon in Dollars 3.80 3.60 3.40 3.20 Point of Inflection 3.00 2.80 2.60 This section is Concave down 2 4 6 8 10 12 14 16 18 20 22 24 or Week This section is Concave up or Average weekly gas prices in the Metro Atlanta area from May 1, 2008 – Nov 1, 2008 Properties of graphs: Concavity 

  29. Stock Market Performance The Dow Jones Industrial Average 13 12 Dow Jones Average (in thousands of dollars) 11 10 9 2000 2001 2002 2003 2004 2005 2006 2007 2008 y = year Does this graph have a point of inflection?

  30. Homework: Read Section 1.3 (omit pages 69-74) Page 75 # S-1 through S-10 Pages 76–79 # 2, 5, 11

More Related