Identify growth/decay factor, growth/decay rate and ... 4... · PDF fileIdentify...

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  • 1

    WarmupOnStudentNotesforDay3

    Identifygrowth/decayfactor,growth/decayrateandinitialvalue

    (AthroughH)

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    Standard6.3WritingExponentialEquations

    Standard6.3 Proficient:Writeexponentialgrowthanddecaymodelsfromcontextandmakepredictions.Expert:Writeexponentialequationsgivenatable.

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    growth/decay:

    factor:

    initialvalue:

    rate:

    Identifygrowth/decayfactor,growth/decayrateandinitialvalue

    (AthroughH)

    A. B.

    C. D.

    E. F.

    G. H.

    growth/decay:

    factor:

    initialvalue:

    rate:

    growth/decay:

    factor:

    initialvalue:

    rate:

    growth/decay:

    factor:

    initialvalue:

    rate:

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    Review:Calculategrowthfactorfrom%increase:

    I. J. K. L.50% 5% 0.5% 0.05%

    Calculatedecayfactorfrom%decrease:

    M. N. O. P.50% 5% 0.5% 0.05%

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    ContextProblems

    Example1A.Youstartawalkingprogram.Youstartbywalking2miles.Theneachweekyouincreaseyourdistance5%perweek.Writeanexponentialgrowthfunctiontomodelthesituation.Howfarwillyouwalkinthetenthweek?

    Generalequation:

    Initialvalue:

    Growthrate:

    Growthfactor:

    Finalequation:

    Prediction:

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    Example1B.Aninitialpopulationof20micetripleseachyearfor8years.Writeanequationthatmodelsthispopulation.Whatisthemousepopulationafter5years?

    Generalequation:

    Initialvalue:

    Growthrate:

    Growthfactor:

    Finalequation:

    Prediction:

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    Example2A:Youboughtacarfor$16,000.Youexpectthecartolosevalue,ordepreciate,atarateof12%peryear.Writeanexponentialdecaymodeltorepresentthissituation.Howmuchwillthecarbeworthin3years?

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    Example2B:Membershipinanafterschoolathleticclubdeclinedatarateof5%peryearfortheperiod20002005.Therewere54membersin2000.Identifytheinitialamount,thedecayrate,andthedecayfactor,thenwriteanequationthatdescribesthissituation.Inwhatyeardidtheclubhave45members?

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    Example1C:Amusicianissavingmoneytobuyanewsnaredrum.Themusicianputs$100inasavingsaccountthatpays3%annualinterestcompoundedyearly.Writeafunctionthatmodelstheamountofmoneyintheaccountovertime.Themusicianwantsadrumthatcosts$149.95.Willtherebeenoughintheaccountafter3years?Explain.

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    Example2C:Thehalflifeofamedicationisthetimeittakesforthemedicationtoreducetohalfofitsoriginalamountinapatientsbloodstream.Acertainantibiotichasahalflifeofabout8hours.Apatienttakes500milligramsofthemedication.

    Writeafunctionthatmodelstheamountofthemedicationinthepatientsbloodstreamovertime.Howmuchofthe500milligramdosewillbeinthepatientsbloodstreamafter24hours?

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    Example1D:Atreescrosssectionalareatakenataheightof4.5feetfromthegroundiscalleditsbasalareaandismeasuredinsquareinches.Treegrowthcanbemeasuredbythegrowthofthetreesbasalarea.Theinitialbasalareaandannualgrowthratefortwoparticulartreesareshowninthetablebelow.

    WriteafunctionthatmodelsthebasalareaAofeachtreeovertime.Inabouthowmanyyearswillthetreesbethesameheight?

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    ExpertExtras

    ExponentialEquationsfromaTableofData(Expert)

    Step1)Findthegrowth/decayfactorbycalculatingtheratioofoutputs(a.k.a.y2/y1)Step2)Findtheinitialvaluefromthetableofvaluesifthepointwithx=0isgiven,

    sincey=awhenx=0.Ifthisvalueisnotgiven,useoneofthepointstosolvefora.Step3)Writegrowth/decayequationusingcalculatedvaluesforaandb.

    Example3A.Growth/DecayFactor

    InitialValue

    Equation

    Example3B.Growth/DecayFactor

    InitialValue

    Equation

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    3C. 3D.3E.

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