Algebra - Unit 5 - Day 2 - Exponential Functions Day 2 ... ?· Algebra ­ Unit 5 ­ Day 2 ­ Exponential…

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  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    1

    February02,2017

    DONOW

    AlgebraI 02/02/17Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

    Usingcompletesentences,explainyouranswerchoice.

    REGENTS PREP

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    2

    February02,2017

    Usingcompletesentences,explainyouranswerchoice.

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    3

    February02,2017

    Real World Examples of Exponential Functions/Growth

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    4

    February02,2017

    RetireaMillionaire?!?Ifyouinvest$1000thisyear,andearn5%interesteachyear,howmuchmoneywillyouhaveafteroneyear?Twoyears?

    Sixyears?Sixtyyears?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    5

    February02,2017

    Ifyouinvest$1000thisyear,andearn5%interesteachyear,howmuchmoneywillyouhaveafteroneyear?Twoyears?

    Sixyears?Sixtyyears?

    TheLOOOOOOOOOOOOOOOOONGway

    year0

    year1

    year2

    year3

    year4

    year5

    year6

    1,000

    1000+1000(.05)1,0001,050

    1050+1050(.05) 1,102.50

    1102.5+1102.5(.05) 1,157.63

    1157.63+1157.63(.05) 1,215.51

    1,276.281000*(1.05)5

    1000*(1.05)6 1,340.10

    year60 1000*(1.05)60 18,679.19

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    6

    February02,2017

    Exponential Growth

    startingamount

    y=abx

    Exponentialgrowthcanbemodeledwiththefunction:

    Thebase,orgrowthfactor,isalwaysgreaterthan1forexponentialgrowth.

    exponent,usually#years

    amountaftertime

    Ifyouinvest$1000thisyear,andearn5%interesteachyear,howmuchmoneywillyouhaveafteroneyear?Twoyears?

    Sixyears?Sixtyyears?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    7

    February02,2017

    Exponential Growth ~ Money

    Youinvested$475inanaccountthatearnsan8.5%interestrate.Howmuchmoneywillyouhaveattheendof12years?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    8

    February02,2017

    Exponential Growth ~ PopulationIn2000,Florida'spopulationwasabout16million.Since2000,thestate'spopulationhasgrownabout2%eachyear.FindFlorida'spopulationin2007.

    AsaClass?

    WithPartner?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    9

    February02,2017

    Exponential Growth ~ PopulationIn2000,Florida'spopulationwasabout16million.Since2000,thestate'spopulationhasgrownabout2%eachyear.FindFlorida'spopulationin2007.

    y=16,000,000(1.02)7102%asadecimal(growthfactor)

    numberofyearssince

    2000

    Formulay=abxUseanexponentialfunction

    Define Leta=theinitial(starting)population,variables Letb=thegrowthfactor,whichis100%+2%=

    102%=writtenasadecimalLetx=thenumberofyearssince2000,Lety=thecurrentpopulation

    Substitute

    Solveuseacalculator

    Florida'spopulationin2007wasabout

    18,378,971people

    startingamount

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    10

    February02,2017

    Howdowefindthebaseforanexponentialgrowthfunctionthatinvolvespercentage?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    11

    February02,2017

    2)Supposeyourparentsdeposited$1500inanaccountearning3.5%interestcompoundedannually(onceayear)whenyouwereborn.Findtheaccountbalanceafter18years.

    1)Aspeciesofrare,deepwaterfishhasanextremelylonglifespanandrarelyhavereproduce.Ifthereareatotalof821ofthistypeoffishandtheirgrowthrateis2%eachmonth,howmanywilltherebeinhalfofayear?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    12

    February02,2017

    2)Supposeyourparentsdeposited$1500inanaccountearning3.5%interestcompoundedannually(onceayear)whenyouwereborn.Findtheaccountbalanceafter18years.

    1)Aspeciesofrare,deepwaterfishhasanextremelylonglifespanandrarelyhavereproduce.Ifthereareatotalof821ofthistypeoffishandtheirgrowthrateis2%eachmonth,howmanywilltherebeinhalfofayear?

    Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

  • AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

    13

    February02,2017

    mathsims.wordpress.comLessonSlides,ResourcesandMore!

    GetaheadstartonyourHomework!!!

    Page 1: Aug 30-5:50 PMPage 2: Mar 13-12:15 PMPage 3: Mar 13-10:00 AMPage 4: Mar 13-12:05 PMPage 5: Mar 13-12:05 PMPage 6: Mar 13-12:05 PMPage 7: Mar 13-12:05 PMPage 8: Mar 13-12:05 PMPage 9: Mar 13-12:05 PMPage 10: Mar 13-10:00 AMPage 11: Jan 3-10:48 AMPage 12: Mar 13-12:07 PMPage 13: Sep 13-5:57 PM

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