Intro to Exponential Functions – Day 8 · Intro to Exponential Functions – Day 8 Recalling...

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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.