Interpreting Scatter Plots · Interpreting Scatter Plots WARM UP Describe the following scatter...
Transcript of Interpreting Scatter Plots · Interpreting Scatter Plots WARM UP Describe the following scatter...
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Distance from the Basket
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Age of House
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MPM1D–Unit4:LinearRelationships–Lesson1 Date:___________Learninggoal:howtocreateandinterpretscatterplots.
InterpretingScatterPlotsWARMUP
Describethefollowingscatterplots:
Tibia Length (cm)
Leg Length (cm)
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ScatterPlotReviewAscatterplotisagraphthatshowsthe_________________________between________variables.Thepointsinascatterplotoftenshowapattern,or_____________________________.Example1:Juliegatheredinformationaboutherageandheightfromthemarkingsonthewallinherhouse.
Age(years) 1 2 3 4 5 6 7
Height(cm) 70 82 93 98 106 118 135
a) Labeltheverticalaxis.b) Describetherelationshipbetweenthe
variables.c) Describethetrendofthedatapoints.
INDEPENDENTANDDEPENDENTVARIABLES
Theindependentvariableislocatedonthe___________axis.Theindependentvariableislocated_________________________inthetableofvalues.Thisvariabledoesnotdependontheothervariable
Independentvariable:______________________________Thedependentvariableislocatedonthe____________axis.Thedependentvariableislocated___________inthetableofvalues.Thisvariabledependsontheothervariable.
Dependentvariable:___________________________________
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Example2:Determinetheindependentvariableandthedependentvariableandthencreateascatterplotforeachsituation.a) Outdoorairtemperatureandamountoficecreamsoldatagrocerystore.IndependentVariable:_________________________DependentVariable:__________________________
b) NumberofstudentscrossingAdlerStreetandthetimeofday.
c) Thedayofthemonthyouwerebornandthelastdigitofyourphonenumber.
d) Aperson’sageandtheiraverageyearlyincome.
Example3:Comparethefollowingtwoscatterplots,thefirstoneiscorrect,thesecondoneisnot.Listtherequirementwhencreatingascatterplot. Justin’sWalk
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Example4:Thefollowingtablecomparesthenumberofhoursthatastudentspentstudying,andtheirtestscore.a) Whatdoesonesquarerepresentonthex-axis?b) Whatdoesonesquarerepresentonthey-axis?c) Createascatterplotofthedata:
d) Whatisthedependentvariable?Howdoyouknow?Whatistheindependentvariable?Howdoyou
know? e) Circlethepointonthegraphthatdoesnotseemtofollowthetrend.Thisiscalledanoutlier.Givea
possibleexplanationforthispoint.f) Therearethreepointswithanx-valueof7.Howisthispossible?g) Isiteasiertoseetherelationshipinthetableofvaluesorinthegraph?Explain.h) Describestherelationshipshownbythedata.
StudyHours TestScore3 805 902 756 807 901 506 152 657 851 407 100
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Assignment4.1:InterpretingScatterPlots1. Supposeyouweretosurveyyourclassmatestoseeifthereisarelationshipbetweenmathmarksandthe
numberofhoursspentwatchingTV.a) Whatcolumnheadingwouldyouuseinatableofvaluesdesignedtoorganizethedatafromyour
survey?b) Whichvariablewouldyouchooseastheindependentvariable?Explainc) Howwouldyouinterprettheorderedpair(2,65)ifitweretoappearonascatterplotofyourdata?
2. Thescatterplotshowsthesalesofbottlewatera
refreshmentboothatthefarmer’smarketfordifferentdaysduringthesummer.
a) WhatinformationdoespointArepresent?b) WhatinformationdoespointBrepresent?c) Whatdoesthescatterplotshowaboutthe
relationshipbetweenthevariables?3. Asurveyof200studentsfindsoutthatstudentsneed
lesssleepastheygetolder.a) Identifytheindependentvariableandthe
dependentvariable.b) Sketchascatterplotofthissituation.
4. Considerthegraphshownonright.Whichrelationshipismostlikelytobe
representedbythisgraph?Explainyourchoice
a) heightvs.weightb) payvs.numberofhoursworkedc) gasremainingvs.distancetravelledd) volumeofwaterinabucketvs.itsmass
5. Thetablebelowshowstheheightofsomegrade9boysandtheirfathers.
a) Identifytheindependentvariableandthedependentvariable.b) Constructascatterplotforthedata.c) Doesthescatterplotsuggestarelationshipbetweenaboy’sheightandhisfather’sheight?Explain.
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MPM1D–Unit4:LinearRelationships–Lesson2 Date:___________Learninggoal:howtodrawalineofbestfit,interpolate,andextrapolate.
LinesofBestFitandMakingPredictionsWARMUPThegraphbelowrepresentstherelationshipbetweenearningsandtimeworked.
a) Whichpointrepresentsthepersonwhoworkedtheleastamountofhours?
b) Whichpointrepresentsthepersonwhoearnedthemostamountofmoney?
c) Whichpointrepresentsthepersonwhohasthehighestrateofpay?
a)Howmanyhourswheredrivenwhen40passengerswereaboardthebus?b)Howmanypassengerswereaboardthebusafter10hourswheredriven?c)Howmanypassengerswereaboardthebusafter6hourswheredriven?Isthisanswertorealistic?Whyorwhynot?
d)Canyoudeterminehowmanypassengerswereaboardthebusafter26hourswheredriven?Whyorwhynot?
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MAKINGPREDICTIONSFROMDATAAskateboarderstartsfromvariouspointsalongasteeprampandpracticescoastingtothebottom.Thistableliststheskateboarder’sinitialheightabovethebottomoftherampandhisspeedatthebottomoftheramp.
a)Identifytheindependentvariableandthedependentvariable.Explainyourreasoning.
b)Makeascatterplotofthedata.
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c)Describetherelationshipbetweenthevariables.
d)Identifyanyoutliers.Whatmightcauseanoutlierinthedata?
e)Drawastraightlinethatpassesclosetothedatapoints.
Howmanydatapointslieonyourline?
Aboveyourline?
Belowyourline?
f)Compareyourlinewithtwootherstudents’lines.Areallthreelinesthesame?Whyorwhynot?g)Usingthelinethatyoudrew;predictthespeedoftheskateboarderataninitialheightof1m.h)Willtherestofthestudentsgetthesameanswertoquestiong)asyoudo?Explain.LINEOFBESTFIT
Thelineofbestfitofascatterplotisthelinethatisdrawnonthegraphsothatthedistancefromthelinetoallofthepointsisminimized.Tobeabletomakepredictions,weneedtomodelthedatawithalineofbestfit.
SuccessCriteriaforDrawingaLineofBestFit1. Thelinemustfollowthe_____________________.2. Thelineshould__________throughasmanypointsaspossible.3. Thereshouldbe__________________________________ofpointsaboveandbelowtheline.4. Thelineshouldpassthroughpointsallalongtheline,notjustattheends.5.Thelinemustbedrawnwitha_________________________.
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Example1:Drawalineofbestfitforthescatterplotbelow.
InterpolateWhenyouinterpolate,youaremakingaprediction__________thedata.Thesepredictionsareusuallyfairly_________.ExtrapolateWhenyouextrapolate,youaremakingaprediction_____________thedata.Itoftenrequiresyouto____________theline.Thesepredictionsareless______________.MAKINGPREDICTIONSUseyourlineofbestfittoestimatethefollowing:
Question Answer MethodofPrediction
Astudent’smarkiftheystudiedfor4hours.
Astudent’smarkiftheydidnotstudy.
Howlongastudentstudiedforiftheyreceived60outof100.
Howlongastudentstudiedforiftheyreceived100outof100.
Linesofbestfitareusefulwhenwewanttopredictwhatweexpecttohappen.
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Thinkaboutit:Doyouincludeanoutlierpointinyouconsiderationwhencreatingalineofbestfit?Recall:Wealwaysidentifyanyoutliersbycirclingthepointonthescatterplot.
Youareinterpolatingwhenthevalueyouarefindingissomewherebetweenthefirstpointandthelastpoint.
Youareextrapolatingwhenthevalueyouarefindingisbeforethefirstpointorafterthelastpoint.Thismeansyoumayneedtoextendtheline.
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Example2:Maliarecordsthenumberoficecreamconesshesellseachdayandthemaximumdailytemperature,asshownonthegraph.Accordingtothisgraph,approximatelyhowmanyicecreamconeswillMaliasellonadaywhenthemaximumtemperatureis36°?Justifyyouranswer.Example3:Dechenhasacandy-makingbusiness.Thegraphshowsthetotalnumberofcandieshisbusinesshasproducedbytheendofeachdayforthefirstfourdays.Ifthistrendcontinues,whichofthefollowingpointsrepresentsadaywithmorecandiesproducedthanexpected?
a) (5,500)b) (9,850)c) (10,1300)d) (14,1400)
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Example4:Plotthedataonthescatterplotbelow,choosingappropriatescalesandlabels.
Note:Thesymbol_______isusedtosignala“break”intheaxiswhenthescaledoesnotstartatzerotoavoid
alargeemptyspaceinonecornerofthegraph.a) Drawalineofbestfit.Describethetrendinthedata.b) Predicttheearningsofa29yearold.Whichmethodofpredictiondidyouuse?c) Predicttheearningsofan80yearold.Whichmethodofpredictiondidyouuse?Isthisaccurate?d)Explainwhythedataforagesover65donotfollowthetrendinthedata.
Age Earnings($)
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30 26500
35 29500
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41 35000
45 36000
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60 41000
62 42500
65 43000
70 37000
75 37500
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Assignment4.2:LinesofBestFitandMakingPredictions1. Studythescatterplotbelow,thenanswerthefollowingquestions.
a) Ifyouwereasked,whatwastheherringpopulationwhen4fishermenfished?”Whatwouldbeyouranswer?
b) Butwhatifyouwereasked,“Whatwastheherringpopulationwhen12fishermenfished?”What
wouldbeyouranswer?
c) Couldyougiveananswerifasked,“Whatwastheherringpopulationwhen7fishermenfished?”Ifso,whatwouldbeyouranswer?
d) DrawtheLineofBestFittorepresentthecorrelationofthedatainthegraphabove.
e) NowuseyourLineofBestFittotheherringpopulationwith...
i)4fishermen ii)12fishermen iii)7fishermen iv)18fishermen v)Nofishermen
f) Statewhichtypeofpredictionyouusedinquestione).
g) Howdotheherringpopulationpredictionswith4fishermen,7fishermenand12fishermendifferfromthepredictionswith18and0fishermen?
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2. Defineinterpolation.3. Defineextrapolation.4. GraphthedataanddrawtheLineofBestFit.Describetherelationships.
Forgrapha)
i. Determinetheheightat6years.Isitinterpolationorextrapolation?ii. ii)Determinetheageforaperson75cm.Isitinterpolationorextrapolation?
Forgraphb)
i. Determinethespeedat45min.Isitinterpolationorextrapolation?ii. Determinethetimeat80km/h.Isitinterpolationorextrapolation?
Forgraphc)
i. Determinethemarkifapersonstudiedfor6hours.Isitinterpolationorextrapolation?ii. Determinenumberofhoursrequiredtoobtain95%.Isitinterpolationorextrapolation?
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MPM1D–Unit4:LinearRelationships–Lesson3 Date:___________Learninggoal:howtoidentifypositivevs.negativecorrelationandthestrengthofcorrelation.
CorrelationofDataWARMUPStudythegraphbelow
a)Whatistheindependentvariable?b)Whatdoesthesymbolonthex-axisrepresent?
c)DescribewhatthepointWrepresents?d)Whichpointrepresentsagirlwhoseshoesizeissmallerthanexpectedforagirlofherheight?d)DescribewhattheYrepresents.
Iseachlineofbestfitagoodmodelforthedata?Whyorwhynot?a) b)c)
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Whatiscorrelation?TYPESOFCORRELATION
Ascatterplotshowsa____________correlationwhenthepatternrisesuptotheright.Thismeansthatthetwoquantitiesincreasetogether.
Ascatterplotshowsa____________correlationwhenthepatternfallsdowntotheright.Thismeansthatasonequantityincreasestheotherdecreases.
Ascatterplotshows_____________correlationwhennopatternappears.Hint:Ifthepointsareroughlyenclosedbyacircle,thenthereisnocorrelation.
STRONGvs.WEAK• Ifthepointsnearlyformaline,thenthecorrelationis
___________________.
• Ifthepointsaredispersedmorewidely,butstillformaroughline,
thenthecorrelationis_______________________.
Example1:Writetwokeywordstodescribeeachrelation,thendrawalineofbestfit.
Hint:Tovisualizethis,enclosetheplottedpointsinanoval.Iftheovalisthin,thenthecorrelationisstrong.Iftheovalisfat,thenthecorrelationisweak.
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LINEARORNON-LINEAR
Ifthepointsformarelativelystraightlineonascatterplot,wesaythatthereisa_______________
relationship.
A_________________________ofbestfitcanbeusedtomodelalinearrelationship.
Ifthepointsdonotformarelativelystraightlineonascatterplot,butatrendisstillevident,wesaythatthere
isa_______________relationship.
Example2:Writetwokeywordstodescribeeachrelation,thendrawalineorcurveofbestfit.
Example2:Wouldyouexpectapositivecorrelation,anegativecorrelation,ornoassociationbetweenthetwodatasets?Wherepossible,identifytheindependentanddependentvariable,thensketchascatterplotthatdescribestherelationship.
a)Theamountoffreetimeyouhaveandthenumberofclassesyoutakeb)Thesalesofsnowshovelsandtheamountofsnowfallc)Lengthofababyatbirthandthemonthinwhichthebabywasbornd)Amountofgasremaininginacaranddistancetravelledbythatcar.e)Markonatestandhairlength
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Example3:Thelocalicecreamshopkeepstrackofhowmuchicecreamtheysellversusthetemperatureonthatday,herearetheirfiguresfor12days.
a) Identifythe: IndependentVariable- DependentVariable-
b) Createascatterplotofthedata.
c) IsthisrelationshipLinearorNon–linear?Explain!
d) Describethecorrelation.
e) Ifthetemperatureis20°C,howmuchsalesfromicecreamdidtheshopget?Isthisanexampleofinterpolationorextrapolation?Explainhowyouknow.
f) Iftheicecreamshopmade$350insales,whatisthetemperature?Isthisanexampleofinterpolationorextrapolation?Explainhowyouknow.
IceCreamSalesvsTemperature
Temperature°C
IceCreamSales
14.2° $215
16.4° $325
11.9° $185
15.2° $332
18.5° $406
22.1° $522
19.4° $412
25.1° $614
23.4° $544
18.1° $421
22.6° $445
17.2° $408
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Assignment4.3:CorrelationofData1. ThemanagerofaPetroCanadaservicestationinCollingwoodandBrampton,Ontariochangesthepriceof
unleadedgasolineandrecordstheamountofgassoldperhourateachprice.Theresultsareshowninthetablebelow:
CollingwoodPrice(c/L) 100.2 98.4 96.3 94.5 95 95.9 99.2 102.3Amountsold(L/h) 293 242 264 272 292 289 271 241BramptonPrice(c/L) 100.2 98.4 96.3 94.5 95 95.9 99.2 102.3Amountsold(L/h) 202 227 250 286 278 272 212 183
a)Foreachtown,i.Makeascatterplotofthedata.Drawalineofbestfitifpossible.ii.Describethetrendandcorrelationinthedata.iii.Doesthepriceofgasaffecthowmuchispurchased?
b)HowdoestheBramptondatacomparetotheCollingwooddata?Givereasonsforthedifferences.
2. Wouldyouexpectapositivecorrelation,anegativecorrelation,ornoassociationbetweenthetwodata
sets?Wherepossible,identifytheindependentanddependentvariable.a) Kilometersdrivenonthehighwayversustheamountofgasleftinthetank.b) Temperatureoutsideversusthenumberofpeopleatthebeach.c) Timespentreadingversusthenumberofpagesleftinthebook.d) Timespentexercisingversusweight.e) Bodytemperatureversusthelengthofhair.f) Ageversusheight.g) Ageversusthenumberofteethinyourmouth.
3. Bacteriacangrowveryquickly;hereisatabletoshowhowfastthiscanhappen.
time(inmins) 1 3 5 7 9 11#ofbacteria 5 25 125 250 425 700
a) IdentifytheindependentVariableanddependentvariable.b) Createascatterplotofthedata.c) IsthisrelationshipLinearorNon–linear?Explain!d) Describethecorrelation.e) Howmanybacteriaarethereafter10minutes?Whattechniquedidyouuse?f) Howlongdoesittakefortheretobe500bacteria?Whattechniquedidyouuse?
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MPM1D–Unit4:Relationships–Lesson4 Date:___________Learninggoal:howtointerpretandcreatedistancetimegraphs.
DistanceTimeGraphs
WARMUP
1. Studentstarts1mawayfromtheCBRandwalksawayataconstantspeed(slowly).
2. Studentstarts3mawayfromtheCBRandwalkstowardsataconstantspeed(slowly).
REFLECT
a)Howarethegraphsdifferent?Howaretheyalike?
b)Howdoesthestartingpositionshowuponthegraph?
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3. Studentstarts5mawayfromtheCBRandthenwalksveryquicklytowardsit.
REFLECT
a)Howisthespeedofthewalkershownonthegraph?
b)Howdowecalculateaperson’sspeed? 4. StudentincreasesspeedwhilewalkingtowardstheCBR™.
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5. StudentdecreasesspeedwhilewalkingawayfromtheCBR™.
6. Studentwalksawayfromranger,at2metresstopsfor5seconds,thenreturnsatthesamepace.
a)Whathappensonthegraphifapersonisnotmoving?
b)Doesitmatterwhichdirectionthepersonisfacing?
c)Whatletterofthealphabetcouldyoucreateonadistancetimegraph?Howdoyouknow?
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Distancevs.TimeGraphsSummary
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Example:Describeeachofthefollowinggraphs:Besuretomentiondirection,distance,time,andspeed.Graph 1stsection 2ndsection 3rdsection
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Assignment4.4:DistanceTimeGraphs1.JulieandOsawereexperimentingwithaCBRandmadethesegraphs.Describetheirmotionsusingwordslikeaway,towards,stopped.Youmayalsoincludewordslikefastandslowifapplicable.
2.ThefollowinggraphrepresentstherelationshipbetweenKenny’sdistancefromhomeonabikerideandtime.Describethe3segmentsofKenny’sride.
Segment Distance Time Direction Speed
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3.Jenleftherhouseanddrovetoschoolinthemorning,asshownintheaccompanyinggraph.Explainwhatishappeningduringeachpartofthegraphbelow
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4.ThegraphshowsJorge’sdistancefromhomeashewalkstoschool.Describehiswalkbyfillingintheblanksbelow:
a) FromAtoB,Jorgewalks______________(towards/away)fromhome.Jorgeiswalkingfor____________min.Hewalks_________m.
b) FromBtoC,Jorgeisstillwalking
_____________(towards/away)fromhome.ThesegmentfromBtoCis____________(less/more)steepthanthatfromAtoB.So,Jorge’saveragespeedhasdecreasedandheiswalkingslower.Hewalksfor_______minandtravels_____________m.
c) FromCtoD,thesegmentishorizontal. Thismeansthat
timeispassing,butJorge’sdistance fromhomestaysthesame.Jorgeis_________________for2min.
d) FromDtoE,JorgecontinueshiswalktoschoolataboutthesameaveragespeedasfromBtoC. He
walksfor_________minandtravels_________m.
e) IttakesJorge_________mintowalk________mtoschool.5.ThegraphshowsOlivia’sdistancefromhomeasshewalkstothestoreandback.Completethetablebelowbasedonherwalk.
Section Distance Time Direction Speed
A-B
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6.ThefollowingdescribesIvan’sdrivefromWindsortoToronto:
a)HowmanytimesdidIvanstop? b)Whichstopwasthelongest? c)DuringwhatsectionwasIvantravellingthefastest?Explain howyouknow.
7.ThreestudentsmadethegraphsbelowusingtheCBRmotionsensor,analyzethegraphsandthenanswer
thequestions.Student#1 Student#2 Student#3a) Whichstudentneverstopped?Explainhowyouknow.
b) Whichstudentwalkedtowards,thenstopped?Explainhowyouknow.
c) Whichstudentreturnedtotheirstartingposition?Explainhowyouknow.
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8.Describethemotionofthestudentthatcreatedthisdistancetimegraph.Giveasmuchinformationaspossibleforeachsectionofthegraph.
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MPM1D–Unit4:Relationships–Lesson5 Date:___________Learninggoal:howtointerpretandanalyzegraphs.
InterpretingGraphs
WARMUP
1)WhatishappeningbetweenpointsAandB?2)WhatishappeningbetweenpointsBandC?3)WhatishappeningbetweenpointsCandD?4)WhatishappeningbetweenpointsDandE?5)WhatishappeningbetweenpointsEandF?6)Tellastorythatdescribeswhatishappeninginthegraph.
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InterpretingGraphsExample1:Supposetapwater,flowingfromafaucetataconstantrateisusedtofilleachofthesecontainers.Matcheachofthefollowinggraphswiththeappropriatecontainer.Justifyyourchoice.
Example2:AdrianandJosephdecidedtoraceoneanother.Thegraphshowstheirmotionduringtherace.
a) Overwhatdistancewastheracerun?Whowon?
b) Whogotaheadstart?Howmanysecondswastheheadstart?
c) Whoranfasterduringtherace?
d) ForhowmanysecondshadAdrianbeenrunningwhenhewasovertakenbyJoseph?
e) HowfarfromthestartdidJosephovertakeAdrian?
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Example3:Chrisrunseachdayaspartofhisdailyexercise.Thegraphshowshisdistancefromhomeasherunshisroute.a)WhichsegmentisChristravellingthefastest/slowest? b)Theformulatocalculatespeedisc)Calculatehisrateofchange(speed)foreachsegmentofthegraph.Example4:Thegraphrepresentthedistancebetweenasquirrelandatree,d,inmetres,asafunctionoftime,t,inseconds.Calculatethespeedofeachsectionofthegraph.Showyourwork
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Assignment4.5:InterpretingGraphs1. Ianandhisfriendsweresittingonadeckandeatingsunflowerseeds.Eachpersonhadabowlwiththe
sameamountofseeds.Thegraphsbelowallshowtheamountofsunflowerseedsremainingintheperson’sbowloveraperiodoftime.Writesentencesthatdescribewhatmayhavehappenedforeachperson.a) b) c) d)
2. Indicatewhichgraphmatchesthestatement.Givereasonsforyouranswer.
a)Abicyclevalve’sdistancefromthegroundasaboyridesataconstantspeed.
a) b) c) d)
b)Achildswingsonaswing,asaparentwatchesfromthefrontoftheswing.
3. Liquidispouredatasteadyrateintothebottle
showninthediagram.Asthebottleisfilled,theheight,h,oftheliquidinthebottlechanges.Which ofthefivegraphsbelowshowsthischange?Giveareasonforyourchoice.
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Graph C
Graph B
Graph D
Graph E
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4. 11o’clock,Micha’smothersendshimtothecornerstoreformilkandtellshimtobebackin30minutes.Examinethegraph.
a)Whyaresomelinesegmentsonthegraphsteeperthan
others?b)Calculatetherateofchange(speed)ofeachoftheline
segments:c) Overwhatinterval(s)oftimeisMichatravellingthe
fastest?Comparesteepness,notdirection.d) Overwhatinterval(s)oftimeisMichatravellingthe
slowest?Comparesteepness,notdirection.e) HowlongdidittakeMichatoreachthestore?Howdoyou
know?f) HowlongdidMichastayatthestore?g) HowlongdidittakeMichatogethomefromthestore?h) HowcanyouusethegraphtotellwhichdirectionMichais
travelling?i) DidMichamakeithomein30minutes?Howdoyou
know?5. Thetortoiseandtheharerunaraceagainsteachother.Thedistancetimegraphfortheirraceisshown
below.ThemotionofthetortoiseisshownbythelineAB.ThemotionofthehareisshownbythelineCDEF.
a) Overwhatdistancewastheracerun?b) Whatisthespeedofthetortoise?c) Howmanysecondsofaheadstartdidthetortoisehaveoverthehare?d) DescribewhattheharewasdoingbetweenthepointsCandD,DandE,EandF.e) WhatisthespeedoftheharebetweenthepointsCandD,DandE,EandFf) Howlonghasthetortoisebeenmovingwhenitwasovertakenbythefare?g) Whowontheraceandwhy?
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6. TheinformationshowninagraphdoesnothavetorepresentdistancefromaCBR.Foreachofthefollowing,choosethedescriptionthatmostcloselymatchesthegraph.
(a) (i)Theelevatorstartsonthesecondfloor,goesto
thefifthfloorwhereittakesonpassengersandthengoestotheseventhfloor.
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(ii)Sarahtakeshalfanhourtogetdressedinthemorning,hurriestoherfriend’shousesotheycanwalktothebusstoptocatchthebustowork.
(c) (iii)Astheweathercoolsintheautumn,salesatMatt’sicecreamshophavebeendecreasing.Duringonerainyweekonlytheregularswhoworkinthesamebuildingpurchasedtheirusualsnacks.WhenMattintroducesanewproduct,salesbegintoimprove.
(d) (iv)Daniel’scompanyassetsdecreaseduringthemonthswhenheispreparinghisnewstorebutimprovedramaticallywhenthestoreopens.Whenacompetitoropensanearbystore,Daniel’sfortunestakeadownturn.
(e) (v)Sandyhasbeensavingaregularamounteachweek.Whenshejoinsherfamilyonavacationshespendspartofhersavingsbutresumeshersavinghabitwhenshereturns.
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(vi)Jeff’sstrengthtrainingprogramcallsforhimtoaddtimetohisworkoutgradually.AfterafewweeksJeffdecidestosuddenlyincreasethetimeheisspendingbutfindshecanmaintainbutnotincreasethenewlevelforseveralweeks.Thenheisabletograduallyincreasetheworkouttimeagain.