6.4ExponentialGrowthandDecayExponentialGrowthandDecayFunctionsExponentialgrowthoccurswhenaquantityincreasesbythesamefactoroverintervalsoftime.Example1:UsinganexponentialgrowthfactorTheinauguralattendanceofanannualmusicfestivalis150,000.Theattendanceyincreasesby8%eachyear.

Exponentialdecayoccurswhenaquantitydecreasesbythesamefactoroverintervalsoftime.Example2:IdentifyingexponentialgrowthanddecayDeterminewhethereachtablerepresentsanexponentialgrowthordecayfunctionorneither.Example3:InterpretingexponentialfunctionsDeterminewhethereachfunctionrepresentsanexponentialgrowthordecayfunctionorneither.Identifytherateofchange.

a) ! = 5(1.07)! b)! = 0.2(0.98)! c)! = 5(−0.6)!

Example4:Rewritingexponentialfunctions

a) ! = 100(0.96)!/!

b) ! = (1.1)!!!RealWorldSituations

Example5:WritingaFunctionYoudeposit$100inasavingsaccount(notthesamepiggybank!)thatearns6%annualinterestcompoundedmonthly.Writeafunctionthatrepresentsthebalanceaftertyears.

Example6:SolvingarealworldproblemThetableshowsthebalanceofamoneymarketaccountovertime.a) Writeafunctionthatrepresentsthebalanceaftertyearsb) Graphthefunction.Thengraphthefunctionfromexample5.c) Comparetheaccountbalances

Example7:Solvingarealworldproblem.Thevalueofacaris$21,500.Itloses12%ofitsvalueeveryyear.(a)writeafunctionthatrepresentsthevaluey(indollars)ofthecaraftertyears.(b)Findtheapproximatemonthlypercentdecreaseinvalue.(c)GraphthefunctionfrompartA.Usethegraphtoestimatethevalueofthecarafter6years.Homework7,9,13-18,21,24-30even,33,34,38,57,62,63