Contemporarycollegealgebra.org

Vision Within Every Instructor - Potential Within Every Student Newsletter of the HBCU College Algebra Reform Consortium* lege algebra is a pre-pre-calculus courseand intermediate algebra is a pre-pre-pre- calculus course, statistics from follow-on courses clearly indicate that only a small per- centage of students successfully meet the tra- rary approach focuses on student develop- ment, mathematical reasoning, and problem - - - - - - - - - - - - - - - - - - - - - - - - - - - - the topics taught in …rst year algebra courses.
The Graphical analysis now plays a central role - Courage To Teach, poses four questions that displaying data in charts and scatter plots,I think are particularly appropriate for those generating a model by …tting a curve to awho are teaching …rst year algebra courses scatter plot, and, most importantly, inter-(intermediate algebra, college algebra). With preting graphs. Technology has also greatlya few changes in wording and order, they are: lessened the need for students to master al- gebraic mechanics. The recursive nature of spreadsheets has brought modeling with re- cursive sequences into the contemporary cur- riculum of …rst year algebra courses.
Before considering these questions it is through small group work, class activities, important to understand who our students presentations, projects, etc. has been shownare and the role our course plays in their aca- to be e¤ective means of instruction. Di¤er-demic program. (In the April 2011 issue of ent instructors, of course, structure these ac-the Vision –Potential Newsletter, Shelly Gor- tivities in di¤erent ways. Some, for instance,don clearly noted that the high school student start each class with a 5-10 minute activitytaking intermediate algebra is di¤erent than to help students to transition into thinkingthe college student taking intermediate alge- about mathematics.
bra.) Parker in speaking about "Who is the self Although the traditional view is that col- that teaches?" refers to the following three We form a recursive sequence in which the el- ements are the amounts of amoxicillin in the Then after 1 hour, there would be approx- connected with the largeness of life.
He argues that the three are interdependent and are necessary for e¤ective instruction. He Reduce it to spiritual, it loses its anchor (1/2)12 875 mg ofamoxicillin in the blood and then a use this Newsletter to discuss their views onteaching.
Repeating the half-life argument appliedto d1, we have d2 = (1/2)12 d1 + 875d3 = (1/2)12 d2 + 875 and so on.
concerned about the maintenance dosage (the The recursive sequence isamount of a medication administered to maintain a desired level of the medication in the blood) and the trough level (the mini- Evaluating the …rst few values of this se- mum amount of medication in the blood dur- quence shows that the maintenance level for ing treatment). The maintenance level of a this situation is 875.21 mg. The trough level medication for a particular dosage can be de- is (1/2)12 875 = 0.21 mg.
termined by the steady state of a recursive se-quence in which the elements are the amounts Do the following:of medication in the blood after taking a dose.
The steady state of a sequence is the value a drug is determined by the dosage. Hint: about which the elements of the sequence Experiment with changing the dosage in the cluster. The steady state for a medication recursive sequence in the example and then can usually be determined after taking a few determine the steady state. For instance try Example. Amoxicillin, a mild antibiotic, has mg.
a half-life of approximately one hour and an adult dosage is usually 875 mg every 12 hours. mined by the time interval between doses.
Hint: Experiment with changing the time in- policy changes and incentives from world gov-terval between doses in the example. For in- ernments, the report says, nearly 80 percentstance, determine the trough for time inter- of global energy demand could be met by re-vals of 4, 8, and 16 hours.
newable energy sources by 2050. After exten- c. Determine the maintenance level and sive negotiations, 194 governments adopted trough for an aspirin dosage of 325 mg. as- the report.
pirin tablet 4 times a day. Aspirin has a half- d. Dilantin is an anti-epilepsy drug. Its ing renewable energy technologies and their half-life is approximately 24 hours. A “nor- potential “integration into present and fu-mal” dosage rate is 300 mg daily.
Deter- ture energy systems.” The energy technolo- mine the maintenance level and trough for gies include solar, wind, bioenergy (includ-Dilantin.
ing sources such as wood scavenging in de-veloping countries), geothermal, and ocean,notably excluding nuclear as a source of re- a pad of paper. If you spent a dollar more for of power generation from renewables in thethe pen than the paper, how much did the United States during the …rst quarter of thepaper cost? year (source: Monthly Energy Review).
b. Is it better to get a 10% discount on an item whose price has already been reduced by 30% or to get a 40% discount on the original ing and Urban Development Income Level for low income housing is $20,700 - $34,450 for a then determine whether a quadratic or anhousehold with two persons. Would a per- exponential curve gives the better …t to theson working 40 hours per week, 50 weeks per data. Explain your reasoning (just statingyear, and earning the minimum wage qualify the R2 value is not su¢ cient). Hint: Let t befor low income housing for two people? sumption of the 80% …gure in the SpecialReport on Renewable Energy Sources andClimate Change Mitigation applied to the United States. Explain your reasoning.
Monthly Energy Review that “The Intergov-ernmental Panel on Climate Change” meet-ing (May 2011) in Abu-Dhabi released its [5] Wind PowerSpecial Report on Renewable Energy Sourcesand Climate Change Mitigation at its meet- ing in Abu-Dhabi (May 2011). Given proper sources of energy around the world.
popular because it is abundant and provides c. Using your model, predict the millions many communities with a clean, local source of kilowatt hours generated by wind in 2011.
of electricity, as opposed to imported fossil fu-els. In the United States, which passed Ger-many to become the country producing themost wind power, the Department of Energy [6] Noticeshas estimated that wind power could accountfor 20 percent of the nation’s electricity sup- ply by 2030. (Source: The New York Times, held in Boston, MA, January 4-7, 2012.
The following table shows the amount of elec- trical power (millions of kilowatt hours) gen- erated by wind, world wide 2003-2009.
rary College Algebra 563.584.6358,[melani_moorman@mcgraw-hill.com] tober Newsletter is October 1, 2011.
Opinion articles, suggestions for writing ities, small group out-of-class projects, 4. To subscribe to this Newsletter, write a. Model this data by …tting a curve to the scatter plot of this data. Hint: Let t be b. Explain why your model is reasonable.

Source: http://www.contemporarycollegealgebra.org/newsletters/105SEP11.pdf