NAME DATE SECTION
IntrotoExponentialFunctions–Day8
RecallingPercentChange
Wheels
Ascootercosts$160.
Foreachquestion,showyourreasoning.
1. Thecostofapairofrollerskatesis20%ofthecostofthescooter.Howmuchdotherollerskatescost?
2. Abicyclecosts20%morethanthescooter.Howmuchdoesthebicyclecost?
3. Askateboardcosts25%lessthanthebicycle.Howmuchdoestheskateboardcost?
TaxesandSales1. Youneedtopay8%taxonacarthatcosts$12,000.Whatwillyouenduppayingin
total?Showyourreasoning.
2. Burritosareonsalefor30%off.Yourfavoriteburritonormallycosts$8.50.Howmuchdoesitcostnow?Showyourreasoning.
3. Apairofshoesthatoriginallycost$79areonsalefor35%off.Doestheexpression0.65(79)representthesalepriceoftheshoes(indollars)?Explainyourreasoning.
ExpressingPercentIncreaseandDecrease
Completethetablesothateachrowhasadescriptionandtwodifferentexpressionsthatanswerthequestionaskedinthedescription.Thesecondexpressionshoulduseonlymultiplication.Bepreparedtoexplainhowthetwoexpressionsareequivalent.
descriptionandquestion expression1expression2(usingonlymultiplication)
Aone-nightstayatahotelinAnaheim,CAcosts$160.Hotelroomoccupancytaxis15%.Whatisthetotalcostofaone-nightstay?
160+ (0.15) ⋅ 160
Teachersreceive30%educatorsdiscountatamuseum.Anadultticketcosts$24.Howmuchwouldateacherpayforadmissionintothemuseum?
(0.7) ⋅ 24
Thepopulationofacitywas842,000tenyearsago.Thecitynowhas2%morepeoplethanithadthen.Whatisthepopulationofthecitynow?
Afteramajorhurricane,46%ofthe90,500householdsonanislandlosttheiraccesstoelectricity.Howmanyhouseholdsstillhaveelectricity?
754− (0.21) ⋅ 754
Twoyearsago,thenumberofstudentsinaschoolwas150.Lastyear,thestudentpopulationincreased8%.Thisyear,itincreasedabout8%again.Whatisthenumberofstudentsthisyear?
Day8Summary
Wecanwritedifferentexpressionstocalculatepercentincreaseanddecrease.
Supposeanewphonecosts$360andisonsaleat25%offtheregularprice.Onewaytocalculatethisistofirstfind25%of360,whichis90,andthensubtract$90from$360togetasalepriceof$270.Thesecalculationscanberecordedinthisway:
360− (0.25) ⋅ 360 = 270
Anotherwaytorepresentthiscalculationistonoticethatsubtracting25%ofthecostisequivalenttofinding75%ofthecost.Usingthedistributiveproperty,weknowthat360− (0.25) ⋅ 360canberewrittenas(1− 0.25) ⋅ 360,whichisequalto(0.75) ⋅ 360.