1.9i SOLUTIONS 1
Solution Manual For Applied Calculus,
7th Edition Deborah Hughes-Hallett,
Andrew M. Gleason, Patti Frazer Lock,
Daniel E. Flath Chapter 1-10 and
PSA(A B C D E)
CHAPTER ONE i
SolutionsiforiSectioni1.1
1. (a)i Theistoryiini(a)imatchesiGraphi(IV),iiniwhichitheipersoniforgotiheribooksiandihaditoireturnihome.
(b) Theistoryiini(b)imatchesiGraphi(II),itheiflatitireistory.iNoteitheilongiperiodiofitimeiduringiwhichitheidistanceifromih
omeididinoti changei(theihorizontali part).
(c) Theistoryiini(c)imatchesiGraphi(III),iiniwhichitheipersonistartedicalmlyibutispediupilater.
Theifirstigraphi(I)idoesinotimatchianyiofitheigivenistories.iInithisipicture,itheipersonikeepsigoingiawayifromihome,ib
utihisispeedidecreasesiasitimeipasses.iSoiaistoryiforithisimightibe:iIistartediwalkingitoischooliatiaigoodipace,ibutisinceiIist
ayediupiallinightistudyingicalculus,iIigotimoreiandimoreitireditheifartheriIiwalked.
2. Theiheightiisigoingidowniasitimeigoesion.iAipossibleigraphiisishowniiniFigurei1.1.iTheigraphiisidecreasing.
height
time
Figurei 1.1
3. Thei amounti oficarboni dioxidei isi goingi upi asitimei goesi on.iAi possiblei graphiisishowni iniFigurei1.2.iThei graphi isiincreasing.
CO2
,2 ChapteriOnei /SOLUTIONS
time
Figurei 1.2
, 1.9i SOLUTIONS 3
4. Theinumberi ofiairiconditioningi unitsisoldiisigoingiupiasitemperatureigoesiup.iAipossibleigraphiisishowniiniFigurei1.3.iT
heigraphi isiincreasing.
ACiunits
temperature
Figurei1.3
5. Theinoiseileveliisigoingidowniasidistanceigoesiup.iAipossibleigraphiisishowniiniFigurei1.4.iTheigraphiisidecreasing.
noiseilevel
distance
Figurei 1.4
6. Ifiweiletitirepresentitheinumberiofiyearsisincei1900,ithenitheipopulationiincreasedibetweeniti=i0ianditi=i40,istayedia
pproximatelyiconstantibetweeniti=i40ianditi=i50,iandidecreasediforiti≥i50.iFigurei1.5ishowsioneipossibleigraph.iManyioth
eri answersiareialsoipossible.
population
years
20i i i 40i i i 60i i 80i i 100i i 120i sincei1900
Figurei1.5
, 4 ChapteriOnei /SOLUTIONS
7. Amounti ofi grassi Gi =i fi(r)i increasesi asi thei amounti ofi rainfalli ri increases,i soi fi(r)i isi ani increasingi function.
8. Weiareigiveniinformationi aboutihowi atmospherici pressureiPi =i fi(ℎ)i behavesi whenitheialtitudeiℎidecreases:iasialtitudei
ℎidecreasesitheiatmosphericipressureiPiincreases.iThisimeansithatiasialtitudeiℎiincreasesitheiatmosphericipressureiPi
decreases.i Therefore,iPi =i fi(ℎ)i isiaidecreasingifunction.
9. WeiareigiveniinformationiaboutihowibatteryicapacityiCi=ifi(Ti)ibehavesiwheniairitemperatureiTidecreases:iasiTidecreases,i
batteryicapacityiCi alsoidecreases.iThisimeansithatiincreasingitemperatureiTi increasesibatteryicapacityiC.iTherefore,i
Ci =i fi(Ti)i isianiincreasingifunction.
10. Timei Ti =i fi(m)i increasesi asi mi increases,i soi fi(m)i isi increasing.
11. Thei attendancei Ai =i fi(Pi)i decreasesi asi thei pricei Pi increases,i soi fi(Pi)i isi ai decreasingi function.
12. TheicostiofimanufacturingiCi=ifi(v)iincreasesiasitheinumberiofivehiclesimanufacturediviincreases,isoifi(v)iisianiincreasingifu
nction.
13. Weiareigiveniinformationiaboutihowicommutingi time,iTi =i fi(c)ibehavesi asitheinumberi oficarsionitheiroadici decreases:iasi
cidecreases,icommutingitimeiTi alsoidecreases.iThisimeansithatiincreasingitheinumberioficarsionitheiroadiciincreasesico
mmutingitimeiTi.iTherefore,iTi =i fi(c)i isianiincreasingifunction.
14. Theistatementifi(4)i=i20itellsiusithatiWi =i20iwheniti=i4.iIniotheriwords,iini2019,iArgentinaiproducedi20imillionimetriciton
siofiwheat.
15. (a)i Ifiweiconsideritheiequation
Ci =i 4Ti −i160
simplyi asi ai mathematicali relationshipi betweeni twoi variablesi Ci andi Ti,i anyi Ti valuei isi possible.i However,i ifi wei thinkio
fiitiasiairelationshipibetweenicricketichirpsianditemperature,itheniCicannotibeilessithani0.iSinceiCi =i 0ileadsitoi0i
=i4Ti−i160,iandisoiTi=i40iF,iweiseeithatiTicannotibeilessithani40iF.iIniaddition,iweiareitoldithatitheifunctioniisin
otidefinediforitemperaturesiabovei134i .iThus,iforitheifunctioniCi =i fi(Ti)iweihave
Domaini =i AlliTi valuesibetweeni40i Fiandi134i F
=i AlliTi valuesiwithi40i ≤iTi ≤i134
=i [40,i134].
(b) Again,iifiweiconsideriCi=i4Ti−i160isimplyiasiaimathematicalirelationship,iitsirangeiisiallirealiCivalues.iHowever,iw
henithinkingiofitheimeaningiofiCi=ifi(Ti)iforicrickets,iweiseeithatitheifunctionipredictsicricketichirpsiperiminuteibetwee
ni0i(atiTi =i 40i F)iandi376i(atiTi =i 134i F).iHence,
Rangei =i AlliCi valuesifromi0itoi376
=i AlliCi valuesiwithi0i≤iCi ≤i376
=i [0,i376].
16. (a)i Thei statementi fi(19)i =i 415i meansi thati Ci =i 415i wheni ti =i 19.i Ini otheri words,i ini thei yeari 2019,i thei concentrationi ofi
carbonidioxidei initheiatmosphereiwasi415ippm.
(b) Thei expressioni fi(22)i representsi thei concentrationi ofi carboni dioxidei inithei yeari 2022.
17. (a)i Atipi =i 0,iweiseeiri =i 8.iAtipi =i 3,iweiseeiri =i 7.
(b) Whenipi =i 2,iweiseeiri =i 10.iThus,ifi(2)i =i 10.
18. Substitutingi xi =i 5i intoi fi(x)i =i 2xi +i 3i gives
fi(5)i =i 2(5)i+i3i =i 10i+i3i =i 13.
19. Substitutingi xi =i 5i intoi fi(x)i =i 10xi −i x2i gives
fi(5)i =i 10(5)i−i(5)2i =i 50i−i25i =i 25.
20. Weiwantitheiy-coordinateiofithei graphiatitheipointiwhereiitsix-coordinatei isi5.iLookingi atitheigraph,iweiseeithatithe
y-coordinateiofithisipointiisi3.iThus
fi(5)i =i3.
