2.6 form follows function - math with ms....

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.6

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2.6 Form Follows Function

A Practice Understanding Task

Inourworksofar,wehaveworkedwithlinearandexponentialequationsinmanyforms.Someoftheformsofequationsandtheirnamesare:

LinearFunctionsEquation Name

! = 12 ! + 1

SlopeInterceptForm! = !" + !,wheremistheslopeandbisthe

y-intercept

! = 12 ! − 4 + 3

PointSlopeForm! = ! ! − !! + !!,wheremistheslopeand(x1,y1)thecoordinatesofapointontheline

! 0 = 1, ! ! = ! ! − 1 + 12

RecursionFormula! ! = ! ! − 1 +D,

Givenaninitialvaluef(a)D=constantdifferenceinconsecutiveterms

(usedonlyfordiscretefunctions)

ExponentialFunctionsEquation Name

! = 10(3)! ExplicitForm! = !(!)!

! 0 = 10, ! ! + 1 = 3! !

RecursionFormula! ! + 1 = !" !

Givenaninitialvaluef(a)R=constantratiobetweenconsecutiveterms

(usedonlyfordiscretefunctions)

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Knowinganumberofdifferentformsforwritingandgraphingequationsislikehavingamathematicaltoolbox.Youcanselectthetoolyouneedforthejob,orinthiscase,theformoftheequationthatmakesthejobeasier.Anymasterbuilderwilltellyouthatthemoretoolsyouhavethebetter.Inthistask,we’llworkwithourmathematicaltoolstobesurethatweknowhowtousethemallefficiently.Asyoumodelthesituationsinthefollowingproblems,thinkabouttheimportantinformationintheproblemandtheconclusionsthatcanbedrawnfromit.Isthefunctionlinearorexponential?Doestheproblemgiveyoutheslope,apoint,aratio,ay-intercept?Isthefunctiondiscreteorcontinuous?Thisinformationhelpsyoutoidentifythebesttoolsandgettowork!

1. Inhisjobsellingvacuums,Joemakes$500eachmonthplus$20foreachvacuumhesells.WritetheequationthatdescribesJoe’smonthlyincomeIasafunctionofthen,thenumberofvacuumssold.

Nametheformoftheequationyouwroteandwhyyouchosetousethatform.

Thisfunctionis: linear exponential neither (chooseone)

Thisfunctionis: continuous discrete neither (chooseone)

2. Writetheequationofthelinewithaslopeof-1throughthepoint(-2,5)Nametheformoftheequationyouwroteandwhyyouchosetousethatform.







3.Writetheequationofthegeometricsequencewithaconstantratioof5andafirsttermof-3.




3. Writetheequationofthefunctiongraphedbelow:




4. ThepopulationoftheresorttownofJavaHotSpringsin2003wasestimatedtobe35,000peoplewithanannualrateofincreaseofabout2.4%.WritetheequationthatmodelsthenumberofpeopleinJavaHotSprings,witht=thenumberofyearsfrom2003?








5. Yessica’ssciencefairprojectinvolvedgrowingsomeseedstoseewhatfertilizermadetheseedsgrowfastest.Oneideashehadwastouseanenergydrinktofertilizetheplant.(Shethoughtthatiftheymakepeopleperky,theymighthavethesameeffectonplants.)Thisisthedatathatshowsthegrowthoftheseedeachweekoftheproject.Week 1 2 3 4 5Height(cm) 1.7 2.9 4.1 5.3 6.5Writetheequationthatmodelsthegrowthoftheplantovertime.Nametheformoftheequationyouwroteandwhyyouchosetousethatform.



Anequationgivesusinformationthatwecanusetographthefunction.Pickouttheimportantinformationgivenineachofthefollowingequationsandusetheinformationtographthefunction.

6. ! = !! ! − 5

Whatdoyouknowfromtheequationthathelpsyoutographthefunction?





7. ! = 2!

8. ! = −2 ! + 6 + 8

9. ! 1 = −5, ! ! = ! ! − 1 + 1





2.6 form follows function - math with ms....

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