Functions and change : a modeling approach to college algebra

645 Pages·2010·6.638 MB·English

by  Bruce Crauder, Benny Evans, Alan Noell

Index of Applications
ASTRONOMY Periodsofplanets,433,436 Trafficspacing,465
Planetarymotion,433,436 Urbantransitspeed,504
Ageoftheuniverse,104
Polaris,36 Waitingtimeintraffic,465
AlphaCentauri,36,430
Quasars,151
Angulardiamater,256
Relativistictime,82
Artificialgravity,148 BIOLOGY
Saroscycles,244
Astronomy,354,361,371,388,430,
Alexander’sformula,148
Sirius,36
446,451
Animalbasalmetabolicrate,447
Spectroscopicparallax,366,371
Binarystars,430
Animalmetabolicweight,447
Speedoflight,83,97
Brightnessanddistanceofstars,354,
Animalmetabolismandsurfacearea,
Stars,354,361,369,388
388
448
Stellardistances,36
Brightnessofstars,35,361,369 Animalmigration,464
Supergiantstars,82
Cosmology,151 Antsrunningspeed,167
Telescopes,264
Distanceofplanets,436 Bacterialgrowth,310
Telescopemagnification,264
Distanceofstars,451 Baldeagle,341
UmbraoftheEarth,225
Distanceofsun,97 Bighornsheep,533
Umbraofthemoon,225
Dopplerblueshift,151 Biomass,457
Universalgravitationalconstant,432
Dopplereffect,151 Birdflight,503
ViewingEarthfromspace,149
Dopplerredshift,151 Bison,150
Weightonthemoon,16
Earthorbitlength,15 Boronuptakebyplants,300
Whitedwarfstars,82
Earthradiusandcircumference,15 Buffalo,150
Eclipses,244 Buffalopopulationgrowth,150
Eratosthenes’measurementofthe AUTOMOBILESAFETY Caloriccontentofmollusks,355
circumferenceoftheEarth,264 Accidentreconstruction,168 Carbondioxideconcentrationsin
FreefallonMars,544 Accidentsandspeed,484,500 greenhouses,80
Geostationaryorbits,432 Automobileacceleration,262 Carlson’syeastexperiment,43
Giantstars,82 Automobileaccident,168 Carryingcapacity,77,118,121
GravityonMars,260,432 Drivingspeedoncurves,241 Championtrees,449
GravityonVenus,432 Emergencystoppingdistance,430 Cohort,456
Hertzsprung-Russelldiagrams,82 Hydroplaning,445 Competitionbetweenpopulations,
Hubble’sconstant,103 Skidmarks,427 169,300,562
Hubble’slaw,103 Skidmarksversusspeed,430 Cornproductionandnitrogen,81
Kepler’sthirdlaw,19,427,433,436 Stoppingdistance,442,443 Costoftransport,451
Lifeexpectancyofmainsequence Tireinflationandaccidents,445 Decayofforestlitter,466
stars,430 Traffic,445 Dinosaurhipheight,148
Lifeonotherplanets,244 Trafficaccidentreconstruction,430 Dinosaurstridelength,148
Luminosityofstars,82 Trafficaccidents,484,500 Dinosaurs,148
Mainsequencestars,82 Trafficcongestion,504 Dispersionofanimals,370
Mass-luminosityrelationforstars,446 Trafficdelay,465 Druginbloodstream,207
Newton’slawofgravitation,427,431 Trafficdensity,356 Eagles,533
OrbitofMercury,433 Trafficflow,326,356,464,465,504 Energycostofrunning,285
OrbitofNeptune,433 Trafficinjuriesandspeed,355 Epidemic,305
Parallax,36 Trafficlights,503,567 Exponentialpopulationgrowth,324,
Parallaxangleofstars,451 Trafficplanning,504 550
Parsecs,366 Trafficqueues,504 Falconglidingspeed,503
PenumbraoftheEarth,225 Trafficsafety,241,244,355,430,464, Fechner’slaw,360
Periodofasatellite,432 503 Flightspeedversuslength,446
Periodsofbinarystars,430 Trafficsignals,19,244 Flyinganimals,446
Foxpopulationgrowth,128,180,205 Photosynthesis,79,325 Yellowfintunagrowthrate,411
Functionalresponse,146 Pigeonglidingspeed,206,503 Yellowfintunapopulationgrowth,416
Functionalresponsecurve,184,492 Plantgrowth,149,168 Yellowstoneelkpopulation,415
Generationtime,437,452 Plantyield,450 Yieldresponse,37
Genetics,501 Populationextinction,466
GeorgeReserve,112,172,205 Populationgenetics,501,502
BUSINESS
Giantantsandspiders,432 Populationgrowth,299
Gompertzpopulationgrowthmodel, Populationgrowth-stochastic,343 AcceleratedCostRecoverySystem
417 Populationthreshold,562 taxdepreciation,59
Grainbeetles,83 Powerneededtofly,502 ACRStaxdepreciation,59
GraywolvesinMichigan,467 Proteincontentofwheat,80 Adjustableratemortgage,39
Grazingkangaroos,182 Proteininfeedmix,299 Amortization,108
Grazingrabbitsandsheep,183,353, Redkangaroo,183 Amortizationtable,126,127
387,563 ReindeeronSt.MatthewIsland,540 Annualpercentageyield,55
Greenhousecarbondioxide Relativeabundanceofspecies,373 Annuity,147
concentrations,80 Renewableresources,399 APR,6,55,126,326,551
Growthinheight,56,242 Respirationandtemperature,464 APY,55,326
Growthinheightandweight,167 Ricecropweight,284 Basicorderquantitymodel,127,502
Growthinweight,51,56 Riceplants,79 Bracketcreep,265
Growthofbacteria,280 RiceyieldsinAsia,285 Break-evenpoint,100,125,167,181,
GrowthofE.colibacteria,325 Runningspeedversuslength,276, 184,206,241
Growthrateversusweight,446 282,350 Budgetconstraints,243
Hill’slaw,505 Runningspeedversustemperature, Canadiandollar,76
Holling’sfunctionalresponsecurve, 283 Canoerental,116
184 Satiationlevel,183 Carrental,99,153
Lengthandweightoffish,276,456 Secondcousins,502 Carresalevalue,145
Lengthversusageforfish,206,353, Self-thinningofplants,450 Carryingcost,127
387 Snakelength,237 Cateringaconvention,183
Lidocaineinjection,207 Soilmoisture,80 Cateringadinner,102
Logisticfunction,121 Spanoflife,84 Cellphones,108
Logisticgrowth,399 Speciescompetition,169 Compoundinterest,6,55,314,550
Logisticgrowthcurve,401 Species-arearelation,125,421,450 Consumerdemand,237
Logisticgrowthofparamecium,414 Stridelengthandspeed,429 Consumerloan,24,35,127,147,182,
LogisticmodelforAfricanbees,414 Sunflowergrowth,137 550
Logisticpopulationgrowth,34,77, Survivorshipcurve,83 Continuouscompounding,34,127,
108,128,172,180,205,554, Swimminganimals,447 147,327
560 Swimmingspeedversuslength,447 Costprice,14
MacArthur–WilsonTheoryof Terminalvelocityofamouse,431 Creditcards,393
Biogeography,324 Terminalvelocityofasquirrel,431 Currencyexchange,63,76,241,299
Metabolism,447 Treeheight,237 Demandforwheat,262,300
Mitscherlich’sequation,37 Tubewormgrowth,38,184,343 Discountrate,464
Normallydistributedpopulation Vision,360 Domesticautosales,282
increase,466 vonBertalanffymodel,206,353,387 DowJonesIndustrialAverage,21
Numberofspeciesversusarea,421 Waterfleapopulationgrowth,184, EAR,55,126,326
Optimumyieldlevel,400 202,407 Economicorderquantitymodel,146
Ospreys,475 Weightgainofanimals,370 Equilibriumprice,165,238
Oxygenconsumption,285,451 Wellhead,103 Federalincometax,264
Pacifichalibutpopulationgrowth,416 Westerngreykangaroo,182 Financingacar,35
Pacificsardinepopulation,401 Wheatproteincontent,80 Fixedcosts,100,240,260,486
Pacificsardinepopulationgrowth,416 WolvesinWisconsin,356 Futurevalue,13,14,464
Photiczoneintheocean,325 Yeastpopulationgrowth,43,106 Germanmark,63
Grossdomesticproduct,53,163,389 Supplyanddemand,165,300 Catchequation,505
Grossnationalproduct,163,282 Supplyofwheat,261,300 Catfishfarm,560
Growthinsales,198 Taxdepreciation,59
Fishpopulationgrowth,197
Homeequity,17,38,59,82,185 TaxReformActof1986,59
Growthinfish,150
Incometax,33,56,167,228,237, Taxtables,264,306
Growthoffishbiomass,200
255,263,276 Teachersalaries,299
Growthofhaddock,129,355
Incometaxbracketcreep,265 Totalcost,91,100,240,260,486
Inflation,324,350 Totalrevenue,100,241,260,486 GrowthofNorthSeasole,206,353,
Inflationrate,79 Tradediscount,14 387
Interestrates,343 TruthinLendingAct,15 Marinefishery,197
Inventorycost,127 Tuitionatprivateuniversities,259 NorthSeacodgrowth,201
Inventoryexpense,502 Tuitionatpublicuniversities,259
NorthSeaplaice,200
Isocostequation,164 Unattainedsales,198
Populationgrowthofmarinefisheries,
Laborproductivity,135 Variablecost,100,240,260,486
Lifeinsurancerates,83 Wageincreases,343 482
Lifespan,84 Widgetproduction,58 Rateofgrowthoffish,201
Loanoriginationfees,104 Rickermodel,201
Logisticmodelforsales,414 Sardines,554
EARTHQUAKES
MARCStaxdepreciation,59
Sockeyesalmon,201
Marginalprofit,276,526,528 Californiaearthquakes,130
Spawner-recruitmodel,200
Marginaltaxrate,228,256,263,306, Earthquakedamage,433
WeightandlengthofNorthSeaplaice,
525 Earthquakes,38,130,357,358,369
Marketdemand,237,262 EarthquakesinArizona,369 449
Marketsupply,237,261 EarthquakesinIdaho,369 Weightversuslengthforfish,430
Maximumsalesgrowth,198 EarthquakesinMontana,369 Yellowfintunagrowth,57
Merchandising,14 Faultrupturelength,38
ModifiedAcceleratedCostRecovery Frequencyofearthquakes,357
Systemtaxdepreciation,59 Magnitudeofearthquakes,358 FORESTRY
Monthlyinterestrate,341 Majorearthquake,130 Forestgrowth,187
Monthlypayment,13,127,147 NewMadridearthquake,358 Forestlitter,466
Moore’slawforcomputerchips,369 Structuralfailureofbuildings,433
Forestlitterdecayrates,466
Mortgage,104 Tsunamibores,431
Forestmeanannualgrowth,200
Mortgageclosingcosts,104 Tsunamiwaves,325,430,431
Mortgagepayment,147 Forestrotationage,200
Mortgagepoints,104 Foreststanddensity,371
FIREFIGHTING
Nominalinterestrate,326 Foreststand-densityindex,371
Oklahomaincometax,167 Fireenginepressure,165 Forestyield,187
Perpetuity,147 Firehosedischarge,129
Forestry,78,187,200,371
Presentvalue,14,35,464 Firehosefrictionloss,185
Forestrymanagement,78
Profit,100,125,206,241,260,486 Firehoses,243
Fullystockedforeststands,371
Realestatesales,57,241 Firefighting,102,129,165,185,243,
Retailsales,165 283 Growthofforests,187
Roomrental,101 Headofwater,102 Longleafpines,109
Ruleof72,15 Pumpbackpressure,102 Meanannualgrowth,200
Sales,51 Underwriter’sformula,185 PacificNorthwestDouglas-fir,78
Salesstrategy,165 Waterpressure,102
Proportionsoftrees,449
Savingaccounts,342
Pulpwoodprices,468
Seriesdiscount,14
FISHERIESSCIENCE Sawtimberprices,468
Stockmarket,76,86,532
Stockturnoveratretail,165 Ageandlengthofhaddock,371 Scribnerscale,109
Stockturnoverrate,100 Biomassofhaddock,464 Timberstumpageprices,58
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Functions and Change
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Functions and Change
A Modeling Approach to College Algebra
Fourth Edition
Bruce Crauder / Benny Evans / Alan Noell
Oklahoma State University
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Contents
Preface ix 1.4 FunctionsGivenbyWords 85
ComparingFormulasandWords 85
GettingFormulasfromWords 88
Proportion 90
Prologue: Calculator Arithmetic 1
AnAlgebraicLook:Geometric
Constructions 91
TypingMathematicalExpressions 2
Chapter1Summary 105
Rounding 2
Chapter1ReviewExercises 107
ParenthesesandGrouping 3
MinusSigns 4
SpecialNumbersπ ande 5
ChainCalculations 5 2
Graphical and Tabular
ScientificNotation 7
Analysis 111
AnAlgebraicLook:OrderofOperations 8
ChapterPSummary 18
2.1 TablesandTrends 112
ChapterPReviewExercises 19
GettingTablesfromFormulas 112
OptimizingwithTablesofValues 115
AnAlgebraicLook:Limits 117
1
Functions 21
2.2 Graphs 132
Hand-DrawnGraphsfromFormulas 132
1.1 FunctionsGivenbyFormulas 22
GraphingwiththeCalculator 132
FunctionsofOneVariable 22
TracingtheGraph 133
FunctionsofSeveralVariables 23
ChoosingaViewingWindowinPractical
AnAlgebraicLook:Definitionofa
Settings 133
Function 25
GettingLimitingValuesfromGraphs 137
AnAlgebraicLook:Shiftingand
1.2 FunctionsGivenbyTables 40
Stretching 139
ReadingTablesofValues 40
FillingGapsbyAveraging 40 2.3 SolvingLinearEquations 152
AverageRatesofChange 41
TheBasicOperations 152
SpottingTrends 43
ReversingtheRolesofVariables 154
AnAlgebraicLook:AverageRatesofChange
AnAlgebraicLook:InverseFunctionsand
withFormulas 46
EquationsThatareLinearinOne
Variable 157
1.3 FunctionsGivenbyGraphs 61
ReadingGraphs 61 2.4 SolvingNonlinearEquations 170
ConcavityandRatesofChange 64
TheCrossing-GraphsMethod 170
InflectionPoints 65
TheSingle-GraphMethod 171
DrawingaGraph 66
AnAlgebraicLook:SolvingNonlinear
AnAlgebraicLook:SecantLinesandArea
EquationsbyFactoring 175
Functions 69