calc

[|ti-83 plus]
 * Title:** Graphing Calculators - A Crash Course
 * Presenter:** Holt Wilson
 * Room:** Poe 420
 * Description: Technology tools can support students in understanding complex mathematical ideas as well as assist teachers in making sense of their students' understandings. In this session, we'll explore some basic features of theTI-84 that can support the explorations and understandings of functions outlined in the new NC Essential Standards. **

Tech: Making Meaning for Students and for Teachers @http://www.youtube.com/watch?v=CIJ0CikId8E

NC Essential Standards MA.A.3, MA.A.4, MA.A.5 MBC.A.1, MBC.A.7, MBC.A.7

Studying Functions using the TI-84

Linear Functions Derrick went way over his cell phone limit last month. His grandmother decided to teach him a lesson. He could keep him phone, but he would have to find a cell phone plan and manage the bills for the next year. Since his phone was purchased at AT&T, he decided he would use their services. He discovered that unless he was willing to make a 2-year service agreement, he would have to agree to a prepaid plan. Here are the four AT&T Pay As You Go© plans in the Raleigh area (Retrieved April 4, 2010 from @http://www.wireless.att.com/cell-phone-service/cell-phone-plans/pyg-cell-phone-plans.jsp )

Plan A - $3 Unlimited Calling Plan $0.00 per minute $3 per day, ONLY on days you use the plan

Plan B - $1 Unlimited Calling Plan $.10 per minute $1.00 per day, ONLY on days you use your phone

Plan C - $.25 Simple Plan $.25 per minute N/A

Plan D - $60 Unlimited Talk and Text Feature Package on the Simple Rate Plan N/A
 * $.00 per minute


 * You will be automatically enrolled on Simple Plan. Feature package is good for 30 days, as long as your Account Balance is not expired. Standard $0.25 per minute Simple Plan rate applies if feature package is not purchased or renewed after 30 days. See rate plan brochure for details.
 * Unlimited text messaging package is $19.99 per month


 * 1) Upon inspection, which plan do you think that Derrick should choose? Why?
 * 2) What aspects of the plans determine will determine his monthly bill?
 * 3) How do those factors relate to the monthly cost of each of the four plans?
 * 4) Conduct an analysis of the four plans. Make and support recommendations to Derrick about which plan he should choose.

Quadratic Functions UV rays, the skin cancer-causing portion of the sun’s light, are strongest in the summer. Doctors recommend that people stay indoors for a two-hour period before and after the peak amount of UV rays. The amount of UV rays on a summer day in North Carolina can be modeled by the quadratic function I(x) = -9x^2 + 249x – 1292, where I(x) represents the amount of UV rays in nanometers, x represents the time in hours ( 7 < x < 20, corresponding to 7am and 8pm).


 * 1) What is the peak amount of UV rays on a given summer day? At what time does that occur?
 * 2) According to doctors, when should people stay indoors?
 * 3) From this recommendation, what is a rough estimate “acceptable” UV rays?

Polynomial Functions The function M(x) = -0.287x^3 + 8.8x^2 - 59.843x + 220.7 describes the incidence of measles (per 100,000) for the period 1940-1960 (x = 0 for 1940).


 * 1) In what year was the greatest incidence of measles reported?
 * 2) According to the definition of M(x), what is the y-intercept?
 * 3) Identify periods of increasing /decreasing frequency of the disease.
 * 4) If the function continues to model the disease beyond 1960, when did the incidence of measles approximate zero?
 * 5) What are some variables that may have affected the incidence of measles over the period 1940-1960?

__More Information on Measles:__ > (Source World Health Organization, http://www.who.int/mediacentre/factsheets/fs286/en/index.html) > (Source US Center for Disease Control, @http://www.cdc.gov/nchs/fastats/measles.htm )
 * Vaccine made available in 1963. Only 92% of the population aged 19-35 is vaccinated (CDC)
 * Measles is one of the leading causes of death among young children even though a safe and cost-effective vaccine is available.
 * In 2008, there were 164 000 measles deaths globally – nearly 450 deaths every day or 18 deaths every hour.
 * More than 95% of measles deaths occur in low-income countries with weak health infrastructures.
 * Measles vaccination resulted in a 78% drop in measles deaths between 2000 and 2008 worldwide.
 * In 2008, about 83% of the world's children received one dose of measles vaccine by their first birthday through routine health services – up from 72% in 2000.
 * In 2007, there were 43 new cases of measles in the US.
 * NIH Measles Information http://www.nlm.nih.gov/medlineplus/measles.html#cat1
 * Recent Measles Outbreak @http://www.nlm.nih.gov/medlineplus/news/fullstory_96684.html

Exponential Functions Carbon dioxide data recorded at the Mauna Loa Observatory in Hawaii constitute the longest record of direct measurements of CO2 in the atmosphere. Using data from 1958 – 2009, one can model the amount of CO2 in the atmosphere measured in ppm since then with the function: A(t) = (0.0911)(1.004)^t
 * 1) Interpret the growth parameter of the function.
 * 2) If the trend continues, what will be the amount of carbon dioxide in the year 2020?
 * 3) When does the model predict the amount of CO2 to exceed 400ppm?

Modeling Data In a recent Op-Ed, the New York Times presented [|this graph] and cited the Southern Poverty Law Center study of //Hate Group// // (Source // [] )

Upon investigation, only data for groups defined as “Hate Groups” was available. The data are available since 1997 and are presented below:

(Source @http://www.splcenter.org/get-informed/intelligence-report/browse-allissues/2010/spring/rage-on-the-right )
 * Year || 1997 || 1998 || 1999 || 2000 || 2001 || 2002 || 2003 || 2004 || 2005 || 2006 || 2007 || 2008 || 2009 ||
 * #groups || 474 || 537 || 457 || 602 || 676 || 708 || 751 || 762 || 803 || 844 || 888 || 926 || 932 ||


 * Based on the graphic, what type of function might model these data?
 * Based on the table, describe the relationship between the year and the number of hate groups.
 * Use an appropriate function to model the number of hate groups identified by the SPLC over the last 13 year. How appropriate is the model?
 * Interpret the parameters of the model in context.
 * Use the model to anticipate the number of groups for 2010? For 2020?

For more information:
 * Southern Poverty Law Center Publications - @http://www.splcenter.org/get-informed/publications
 * YouTube video from 2009 @http://www.youtube.com/watch?v=rElqVPbfLM8