资源描述：
《exponential functions and real life problems：指数函数与现实生活中的问题》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、ExponentialFunctionsandRealLifeProblems:Anypositivenumbercanbeusedasthebaseforanexponentialfunction,butsomebasesareusedmorefrequentlythanothers.Bases2and10areoneofthemorefrequentlyusedones.Themostimportantbaseisthenumberdenotedbytheletter.Thenumberisdefinedasthevalue
2、thatapproachesasbecomeslarge.12.0000052.48832102.593741002.704811,0002.7169210,0002.71815100,0002.718271,000,0002.71828Fromthetablewecanseethat,correcttofivedecimalplaces.Infactthevalueofto20decimalplacesis(ThenotationwaschosenbyLeonhardEuler,probablybecauseitisthefi
3、rstletterinthewordexponential)ThenaturalExponentialFunction:istheexponentialfunctionwithbase.Itisoftenreferredtoastheexponentialfunction.Evaluateeachexpressioncorrecttofivedecimalplaces:1)2)3)4)Aninfectiousdiseasebeginstospreadinasmallcityofpopulation10,000.Afterdays
4、,thenumberofpersonswhohavesuccumbedtothevirusismodeledbythefunction:Howmanyinfectedpeoplearethereinitially,afteroneday,twodaysandfivedays?CompoundInterest:iscalculatedbytheformulaWhere:amountafteryearsprincipalinterestrateperyearnumberoftimesinterestiscompoundedperye
5、arnumberofyears5)Asumof$2000isinvestedataninterestrateof7%peryear.Findtheamountsintheaccountafter10yearsifinterestiscompoundedannually,semiannually,quarterly,monthly,anddaily.6)Asumof$1000isinvestedataninterestrateof12%peryear.Findtheamountsintheaccountafter3yearsifi
6、nterestiscompoundedannually,semiannually,quarterly,monthlyanddaily.ContinuouslyCompoundedInterest:iscalculatedbytheformulaWhereamountafteryearsprincipalinterestrateperyearnumberofyears7)Findtheamountafter4yearsif$1100isinvestedataninterestrateof11%peryear,compoundedc
7、ontinuously.Roundtothenearestcent.8)Findthetotalamountofmoneyinanaccountafter2yearsif$100isinvestedataninterestrateof5.5%peryear,compoundedcontinuously.Roundtothenearestcent.
