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

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• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

DONOW

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

REGENTS PREP

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

Real World Examples of Exponential Functions/Growth

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

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

Sixyears?Sixtyyears?

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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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

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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

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February02,2017

Exponential Growth ~ Money

Youinvested\$475inanaccountthatearnsan8.5%interestrate.Howmuchmoneywillyouhaveattheendof12years?

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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AsaClass?

WithPartner?

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

2000

Formulay=abxUseanexponentialfunction

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

Substitute

Solveuseacalculator

18,378,971people

startingamount

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

Howdowefindthebaseforanexponentialgrowthfunctionthatinvolvespercentage?

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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

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

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

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

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

Aim:HowDoWeModelSituationsInvolvingExponentialGrowth?HW:ExponentialFunctionsDay2WS

• AlgebraUnit5Day2ExponentialFunctionsDay2.notebook

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February02,2017

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