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ofAlbertaLibra Module 2 1620 3452411 4 Learning /dlberra Technologies Branch EDUCATION Digitized by the Internet Archive in 2016 with funding from University of Alberta Libraries <*y https://archive.org/details/puremathematics302albe_1 Module 2 Exponents and Logarithms PureMathematics30 Module2: Exponentsand Logarithms StudentModuleBooklet LearningTechnologiesBranch ISBN 0-7741-2798-8 TheLearningTechnologiesBranchacknowledgeswithappreciationtheAlbertaDistanceLearningCentreand PembinaHillsRegionalDivisionNo.7fortheirreviewofthisStudentModuleBooklet. 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Module 1 Transformations Module 2 Exponentsand Logarithms Module 3 SequencesandSeries Module 4 Conics — — J - Module 5 Trigonometry Module 6 Combinatorics Module 7 ProbabilityandStatistics CONTENTS Exponential Logarithmic Functions Functions Activity 1: GrowthandDecay Activity 1: Logarithms Activity2: Exponential Activity2: LawsofLogarithms Equations Activity3: EquationSolving Follow- Activities Follow- Activities Enrichment Enrichment Conclusion Conclusion Assignment Assignment 57 FinalModuleAssignment Glossary 58 60 CalculatorFunctions 61 SuggestedAnswers 63 Credits . ModuleOverview Atthebeginningofthetwenty-firstcentury, Canada’spopulationwasmorethan30million.Thisrepresents abouta5.5-foldincreaseoverthe last 100years, oranannual increase ofapproximately 1.72%. Doyouthink thepopulationwillcontinuetoincrease atthisrate?Whatdoyouthinkthenation’spopulationwillbe atthe endofthetwenty-firstcentury?Assumingthegrowthrate doesnotchange, whatwouldthepopulationbe after 1000years? Populationgrowthis oftenmodelledbyaspecialclass offunctions, calledexponential functions. In Section 1 youwill explorethe exponential functionanditsgraphusingtechnology.Youwillthenuseexponential functionsandequationsarisingfromtheapplicationofexponential functionsto solveavarietyofpractical — problems problemsthatincludepopulationgrowth, compoundinterest, depreciation, andradioactivedecay. In Section2youwill investigateanotherclass offunctions, calledlogarithmic functions.Youwill discoverthat logarithmic andexponentialfunctionsarerelatedandthatmanylaws forlogarithms are similartothe laws for exponents.Youwill applytheselawsandpropertiesto solve equationsandmodelpracticalproblems in growthanddecaysimilartothose introducedin Section 1 Module 2: Exponents and Logarithms i PureMathematics30: Module2 Assessment Thedocumentyouarepresentlyreading iscalleda StudentModuleBooklet. Itwill showyou, stepbystep, whatto doandhowtodo it. Thismodule,Exponents andLogarithms,hastwo sections.Withineach section,yourworkisgroupedinto activities. Withintheactivities,therearereadings andquestions foryoutoanswer. Bycompletingthese questionsyouwillconstructyourownlearning, discovermathematicalconnections, andpractiseorapply whatyouhave learned.The suggestedanswers intheAppendix ofthis StudentModuleBookletwillprovide youwithimmediate feedbackonyourprogress. Inthismoduleyouwillbe directedtothe accompanyingAssignmentBooklets.Youareexpectedto complete twoAssignmentBooklets forthismodule.Yourgradinginthismoduleisbaseduponthe assignmentsthatyou submitforassessment.Themarkdistributionis as follows: AssignmentBooklet2A Section 1Assignment 35 marks AssignmentBooklet2B Section 2Assignment 50 marks FinalModuleAssignment 15 marks TOTAL 100 marks 2