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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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