Download - Integrated Math I Name: Period: Date: CH 4, L5 ONVERT … · 2020. 1. 27. · Integrated Math I Name: ___ Period: _ Date: ___ CFS: 1. Table or sequence is created from the

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Tableorsequenceiscreatedfromthefunction2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsarewritteninlinearorexponentialform4. Functionsarecheckedtobeequivalentbytestingavalue

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CH. 4, L5 – CONVERT BETWEEN EXPLICIT AND RECURSIVE FUNCTION

Objective:Givenafunctionrule,Iwilltranslatebetweenrecursiveandexplicitformulasforthesamesequence.ThinkAboutIt:Rewritethefunction𝑓 𝑥 = −2𝑥 + 14asarecursivefunctionusinganymethod.

Keywords: explicit, recursive

BigIdea:

KeyPoint#1:

Givena____________or_________function,creatinga________ofvaluescanbeusedto___________inthe________form.



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InteractionwithNewMaterial:

Ex.1) Twobankaccountsareearningmoneyatdifferentratesasshowninthetwofunctionsbelow.If𝑓 𝑥 and𝑔(𝑥)representthevalueofeachbankaccountafter𝑥numberofyears,whichaccounthasmoremoneyandbyhowmuchafter15years?

AccountA:

𝒇 𝟏 = 𝟏𝟎𝟓𝟎, 𝒇 𝒙 = (𝟏.𝟎𝟓)𝒇(𝒙− 𝟏)

AccountB:

𝒈 𝟏 = 𝟏𝟖𝟏𝟕.𝟕𝟓, 𝒈 𝒙 = 𝒈 𝒙− 𝟏 + 𝟏𝟕.𝟕𝟓



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PartnerPractice:

1. Writetheexplicitfunctionsasrecursivefunctions:

a. 𝑎 𝑛 = 3𝑛 + 1

b. 𝑎 𝑛 = 2 3 !

c. 𝑎 𝑛 = 𝑛

2. Writetherecursivefunctionsasexplicitfunctions:

a. 𝑎 1 = 5, 𝑎 𝑛 = 𝑎 𝑛 − 1 + 4

b. 𝑎 1 = 3, 𝑎 𝑛 = 2 𝑎 𝑛 − 1

c. 𝑎 1 = 10, 𝑎 𝑛 = !!𝑎 𝑛 − 1



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3. Whichofthefollowingfunctionswillhaveagreateroutputwhennisequalto100?

𝑎 1 = 101, 𝑎 𝑛 = 1.01 𝑎(𝑛 − 1)

𝑏 1 = 101.7, 𝑏 𝑛 = 𝑏 𝑛 − 1 + 1.7

AccountA:

AccountB:

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4. Adamproposesthathismotherchangeshisallowanceaccordingtothefollowingrule:“Thefirstweek,you’llonlygive$0.02.Theneachweekafterthefirstweek,you’llpaytwicewhatyoupaidtheweekbefore.”Hismothersaysthatshewillnotagreetohisplan,insteadsheproposesthatAdamgets$5inallowanceeachweek.i

a. WriteexplicitequationstomodelbothAdamandhismother’splans.

b. Writerecursiveequationstomodelbothoftheplans.

c. WhywouldAdam’smothernotagreetohisplan?Explain.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________



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5. Jamessaves$85.Hewantstoputitinasavingsaccountsoitwillgaininterest.BankLmakesthefollowingoffer:“Ifyoukeepyourmoneywithus,attheendofeveryyearwe’llgiveyou$5.”AcrossthestreetfromBankLisBankE.ItoffersJamesthefollowinginvestmentplan:“Everyyear,we’lladd5%ofthemoneyyouhadthepreviousyeartoyouraccount.”

a. Writeanexplicitequationtomodeltheplansforeachbank.

b. WhichrecursivefunctionsbelowmatchBankLandBankE’splans?Explainhowyouknow.

c. WhichbankoffersthegreaterreturnonJames’smoneyintheshortrun?Inthelongrun?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________



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Download - Integrated Math I Name: Period: Date: CH 4, L5 ONVERT … · 2020. 1. 27. · Integrated Math I Name: _____ Period: _____ Date: _____ CFS: 1. Table or sequence is created from the

Download - Integrated Math I Name: Period: Date: CH 4, L5 ONVERT … · 2020. 1. 27. · Integrated Math I Name: ___ Period: _ Date: ___ CFS: 1. Table or sequence is created from the