Chapter66.1ExponentialGrowthandDecayFunctionsExponentialGrowthandDecayFunctionsDefinitions:

Exponentialfunction:intheformof! = #$%where$ ≠ 1andmustbepositive.ExponentialGrowth:if# > 0#+,$ > 1then! = #$%isanexponentialgrowthfunctionExponentialDecay:if# > 0#+,0 < $ < 1then! = #$%isanexponentialdecayfunctionGrowth/DecayFactor:the“b”valueAsymptote:isalinethatagraphapproachesmoreandmoreclosely.(Doesnottouch!)

Example1:GraphingExponentialGrowthandDecayFunctionsTellwhethereachfunctionrepresentsexponentialgrowthorexponentialdecay.Thengraphthefunction.

a) ! = 2% b)! = /0

%

CriticalThinking:Yougoouttoeatatanicerestaurantandyoureceivethecheck.Thecheckisfor$78andyouwouldliketoleavea20%tip.Calculatethetotalofthecheckandtip.

ExponentialModelsExponentialGrowthModel:! = # 1 + 2 3 ExponentialDecayModel:! = # 1 − 2 3

***IMPORTANTNOTE!Whenusingapercentage“r”isalwayswrittenindecimalform!***

Example2:SolvingaReal-LifeProblemThevalueofacary(Inthousandsofdollars)canbeapproximatedbythemodel! = 25 0.85 3,wheretisthenumberofyearssincethecarwasnew.

a) Tellwhetherthemodelrepresentsexponentialgrowthordecay.

b) Identifytheannualpercentincreaseordecreaseinthevalueofacar.

c) Estimatewhenthevalueofthecarwillbe$8,000.Example3:WritinganExponentialModelIn2000,theworldpopulationwasabout6.09billion.Duringthenext13years,theworldpopulationincreasedbyabout1.18%eachyear.

a) Writeanexponentialgrowthmodelgivingthepopulationy(inbillions)tyearsafter2000.

b) Estimatetheworldpopulationby2005.

c) Estimatetheyearwhentheworldpopulationwas7billion.

Example4:RewritinganExponentialFunctionTheamounty(ingrams)oftheradioactiveisotopechromium-51remainingaftertdaysis! = 0.5 3/09,whereaistheinitialamount(ingrams).Whatpercentofthechromium-51decayseachday?CompoundInterest(Wealllovemoney!)

: = ; 1 + 2+

<3

Example5:FindingtheBalanceinanAccount.Youdeposit$9000inanaccountthatpays1.47%annualinterest.Findthebalanceafter3yearswhentheinterestiscompoundedquarterly.

Homework6,8,9-18(don’tgraph),19-21,24,29-35odd*,38,51