exponential growth and decay指数增长和衰变

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1、ExponentialGrowthandDecayExponentialgrowthanddecayoccurswhenquantitiesincreaseordecreaseproportionaltothequantitypresent.Ex.GrowthDecaySavingsAccountsRadioactiveChemicalsRRSP’sCarbonDatingBacterialCulturesValueofavehiclePopulationGrowthConsideracitythat’spopulationgrowsat5%peryear.Intheyea

2、r2000thepopulationwas100000.2001100000x1.05=1050002002105000x1.05=1102502003110250x1.05=115763n-yearsThefunctionthatexpressesthepopulationafternyearsis.Ex.Avasewaspurchasedin1990for$8000.Ifthevaseappreciatesat6%peryear,howmuch:a.Wasitworthintheyear2000.b.Willitbeworthintheyear2030.Thestand

3、ardformofanexponentialgrowthordecayis.istheinitialamount.bisthegrowth(1+i)ordecay(1-i)factoriisthepercentrateofgrowthordecay(asadecimal).tisthenumberofgrowthordecayperiods(thisdependsonthequestion)Ex.Theworldpopulationdoublesevery35years.Ifthepopulationwas6billionin1999,find:a.Thepopulatio

4、nin2050.b.Whenthepopulationwillbe24billion.Sometimes,youwillbeaskedtofindtherateofincreaseofapopulation.Ex.Thepopulationofatownwas24000in1980,and29000in1990.a.Determineanexpressiontofindthepopulationintyearsafter1980.b.Whatwillbethepopulationin2020?ExponentialDecayEx.Acardepreciatesby15%pe

5、ryear.Ifyoubuyacarfor$15000,findthevalueofthecarin.a)3yearsb)10yearsHalf-LifeEx.Anisotopeofradiumhasahalf-lifeof1620years.Ifyouhave10mg,howmuchwillbeleftin:a)50yearsb)500yearsHomework–Handoutq.1-5,7,8,10,12,14,15