integrated math i name: period: date: ch 4, l5 onvert … · 2020. 1. 27. · integrated math i...
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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.
Integrated Math I Name: ________________________________________ Period: ______ Date: ____________
CFS:1. Tableorsequenceiscreatedfromthefunction2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsarewritteninlinearorexponentialform4. Functionsarecheckedtobeequivalentbytestingavalue
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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
Integrated Math I Name: ________________________________________ Period: ______ Date: ____________
CFS:1. Tableorsequenceiscreatedfromthefunction2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsarewritteninlinearorexponentialform4. Functionsarecheckedtobeequivalentbytestingavalue
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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
Integrated Math I Name: ________________________________________ Period: ______ Date: ____________
CFS:1. Tableorsequenceiscreatedfromthefunction2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsarewritteninlinearorexponentialform4. Functionsarecheckedtobeequivalentbytestingavalue
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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.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Integrated Math I Name: ________________________________________ Period: ______ Date: ____________
CFS:1. Tableorsequenceiscreatedfromthefunction2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsarewritteninlinearorexponentialform4. Functionsarecheckedtobeequivalentbytestingavalue
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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?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Integrated Math I Name: ________________________________________ Period: ______ Date: ____________
CFS:1. Tableorsequenceiscreatedfromthefunction2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsarewritteninlinearorexponentialform4. Functionsarecheckedtobeequivalentbytestingavalue
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