6.4 Exponential Growth and Decay - WordPress.com...Jan 06, 2018 · Exponential decay occurs when a...
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6.4 Exponential Growth and Decay Exponential Growth and Decay Functions Exponential growth occurs when a quantity increases by the same factor over intervals of time. Example 1: Using an exponential growth factor The inaugural attendance of an annual music festival is 150,000. The attendance y increases by 8% each year.
Transcript of 6.4 Exponential Growth and Decay - WordPress.com...Jan 06, 2018 · Exponential decay occurs when a...
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
