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# MULTI MTHSC 207

Clemson

GPA 3.76

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This 12 page Class Notes was uploaded by Jazmyn Braun on Saturday September 26, 2015. The Class Notes belongs to MTHSC 207 at Clemson University taught by Staff in Fall. Since its upload, it has received 87 views. For similar materials see /class/214287/mthsc-207-clemson-university in Mathematics (M) at Clemson University.

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Date Created: 09/26/15

Fall 2008 Name SecTions 55 amp 61 63 UniT 2 PracTice SecTion InsTrucTor General DirecTions Show work where possible Answers wiThouT supporTing work where work is appropriaTe may receive liTTle crediT Do noT round inTermediaTe calculaTions Answers in conTexT ALWAYS require uniTs Round your answers To 3 decimal places UNLESS The answer needs To be rounded differenle To make sense in The conTexT of The problem OR The direcTions specify anoTher Type rounding OR The compleTe answer has less Than 3 decimal places When you are asked To wriTe a model include all componenTs of a model an equaTion a descripTion of The inpuT and uniTs a descripTion of The oquuT and uniTs and The inpuT inTerval when known When asked To wriTe a senTence of pracTical inTerpreTaTion answer The quesTions when whaT how and how much using ordinary conversaTional language Do noT use maTh words Terms or unnecessary phrases Always use a ruler when esTimaTing values off of a graph HINTS FOR TROUBLESHOOTING YOUR CALCULATOR If you lose your L1 L2 eTc you may reinserT Them using STAT 5 seTup ediTor enTer The SCATTER PLOT will noT show unless PloT 1 has been Turned on and There is daTa in L1 and L2 Turn offon scaTTer ploTs by using The arrows To highlighT The iTem you wanT offon and using The enTer key To change The sTaTus DIM MISMATCH error usually means ThaT The lisTs in L1 and L2 are noT of equal lengTh DATA TYPE error usually means ThaT you already have someThing in Y1 and you need To clear iT before you can pasTe a new equaTion INVALID DIM error usually means ThaT your ploTs are on buT ThaT you have no daTa in The lisTs Refer To The second hinT above If your baTTeries die raise your hand and hold up your calculaTor If your insTrucTor has an exTra calculaTor available heshe will loan iT Toyou for a few minutes The NUMINTGL program requires ThaT The funcTion be sTored in Y1 and wriTTen in Terms of x An unexpecTed 0 value when inTegraTing an improper inTegral involving an exponenTial funcTion may mean ThaT you have increased The bounds beyond whaT The calculaTor can compuTe Try smaller boun s NO SIGN CHANGE error usually means you are aTTempTing To solve an equaTion ThaT has no soluTion age I1 Fall 2008 SecTions 55 amp 61 63 UniT 2 PracTice The firsTparT of This TesT consisTs of 15 muTipe choice quesTions Each quesTion has M correcT answer Using a Zpencii bubbe in The e TTer of The response ThaT besT answers each quesTion on your scan Tron For your own record circe your responses and no Te ThaT on This porTion m The scan Tron answers wi be graded This sec Tion wi accounT for 45 of The TesTgrace 1 EvaluaTe Jidx X 1 a 13816 b 20723 c co d 0 2 Charlie jusT won The sTaTe loTTery He has Two opTions for receiving his winnings OpTion 1 The loTTery commission will deposiT a conTinuous sTream of paymenTs inTo an accounT for Charlie over a 30year period which will earn inTeresT aT an annual raTe of 525 compounded conTinuously The guaranTeed 30year fuTure value of The accounT is 20 million OpTion 2 The loTTery commission will give Charlie a oneTime paymenT righT now ThaT is equal To The 30year presenT value of The accounT referenced in The firsT opTion How much money will he receive righT now if he chooses OpTion 2 a 4140 million b 18977 million c 0667 million d 3220 million Widge InTernaTional produces widgeTs and has deTermined ThaT The demand for widgeTs D can be given by 2000 D 50 Thousand WId eTs p 2 9 where The price is p dollars per widgeT Check PoinT D18 50 The graph of Dp is shown below moo BOO 600 00 400 a Thousand widgets 200 o 5 10 15 20 25 30 35 40 Use The informaTion provided To answer The nexT four quesTions Pdalmp My Page I2 Fall 2008 SecTions 55 amp 61 63 UniT 2 PracTice 3 Find The price pt aT which consumers will no longer purchase widgeTs a 850 b 40 c 38 d 950 4 Suppose The currenT markeT price is 2175 per widgeT resulTing in a demand of approximaTely 3421 Thousand widgeTs Which of The following expressions represenTs The Consumers39 Surplus aT The currenT markeT condiTions NoTe pt represenTs The price aT which consumers will no longer purchase widgeTs found in The previous quesTion a b P F 2000 2000 5O 0 50de 21l75 3321 c d 2175 34 21 I 200 504p I 2000 5o m PT 2N5pa 5 ApproximaTely how much will consumers spend for 20 Thousand widgeTs a 818182 Thousand b 26571 Thousand c 40909 Thousand d 5314 Thousand Page I3 Fall 2008 SecTions 55 amp 61 63 UniT 2 PracTice can fexf con rmed from pre VOUS page 6 Which shaded area on The graph of Dp below corresponds To Consumers39 Willingness and AbiliTy To Spend aT a markeT price of 15 per widgeT a b 1000 1000 800 i 600 00 400 q Thousand widge r q thousand widgefs m 8 200 zoo p dalars per widget p dollars per widgef O D 39 1000 39 1000 l q fhousand Widgets m 8 q Thousand 141ng 1 a 8 400 200 200 p dolar per widgef p dalars per widge 7 Sophia sTarTed invesTing in a reTiremenT accounT 20 years ago Her invesTmenT was a conTinuous sTream of R7 7000103 dollars per year where T is The number of years afTer she firsT sTarTed invesTing If The reTiremenT accounT earned 63 annual inTeresT compounded conTinuously over The enTire 20year period whaT is The currenT accounT balance a 10208441 b 67300325 c 19090011 d 35989057 Page I4 Fall 2008 SecTions 55 amp 61 63 UniT 2 Pr39acTice 3 When asked To algebraically evaluaTe I 501210de a sTudenT has reached The following sTep in his work The work in beTween has been inTenTionally omiTTed 73501210de Nlimw5e1 3 5e10N 8 Which of The following is The final r39esulT of The algebr39aic process for39 evaluaTing 3 I 501210de 3 a 50210de eltgt 3 b I 501210de 0 3 c 1501210de 5230 3 d 1501210de ltgtltgt 9 Mike and Anna hope To buy a boaT 10 years from now by invesTing inTo an accounT r39eTur39ning 84 annual inTer39esT compounded conTinuously Assuming a conTinuous income sTr39eam how much will annual invesTmenTs of 25000 dollars per39 year39 be wor39Th 10 years from now a 13232341510 b 168780817 c 16913377 d 39177589 10 The revenue of a small business is 92000 and is expecTed To increase by 9000 each year39 They will invesT 40 of The revenue inTo an accounT in a conTinuous sTr39eam The besT model To explain The income sTr39eam is a RU 36800 90007 dollars per39 year39 b Rf 04 92000 9000f dollars per year39 c 27 92000 140 9000 dollars per39 year39 d RU 92000 90007 dollars per39 year39 Page I5 Fall 2008 SecTions 55 amp 61 63 UniT 2 PracTice 11 A movie renTal sTore made a profiT of 75 Thousand dollars in The year 2000 and expecTs ThaT profiT will increase by 15 each year ThereafTer The sTore managemenT wanTs To invesT 11 of iTs profiTs in an accounT wiTh a 76 APR compounded conTinuously Assuming a conTinuous income sTream which of The following represenTs The sTream of income being invesTed a 2r 75o111015 Thousand dollars per year b 2r 75O110076O985 Thousand dollars peryear c 2r 75o11o015 Thousand dollars per year d 2r 75oo7oo9s5 Thousand dollars per year The willingness of producers To supply fleece hoodies can be modeled as 5p 1007 5 When P 2 5 hundred hoodies 0 when p lt when hoodies are sold for 0 dollars each 12 WhaT does The shuTdown price imply abouT The Producers39 Revenue Producers will noT supply hoodies if They cannoT receive aT leasT 50000 in revenue Producers will receive no revenue aT a price of 5 per hoodie Producers will receive 37500 in revenue if The price is less Than 5 per hoodie Producers will noT supply hoodies if They cannoT receive aT leasT 10000 in revenue 9957 13 Find The markeT price of hoodies when producers supply 230 hundred hoodies a 2295 per hoodie b 1800 per hoodie c 217 per hoodie d 2350 per hoodie Page I6 Fall 2008 Sections 55 At 61 63 Unit 2 Practice Fx thousand dollars gives the proFit or a car dealership x months aFterthe business opened 3 g x g 12 The graph or Fx is shown below 12 7e Area540 Px rm and dollars 12 x month a ar opening 350 14 What was the average proFit oFthe car dealershipFrom 3 to 12 months aFter opening 13 thousand dollars 14 thousand dollars 5 44thousand dollars 66556 thousand dollars RP The rate or change ul 39 39 39 39 rx percent per year where x is the number oFyears aFter 1970 35 Irxd n e n n 35 15 WhlLllUl a From 39 year b From 1970 through 2005 unemployment increased by 0023 percent c From 1970 through 2005 unemployment averaged 0023 percent per year d From 1970 through 2005 unemployment averaged 0023 percent This end or multiple duke poiHon The r Msponsc pmi hum Page l7 Fall 2008 SecTions 55 amp 61 63 UniT 2 PracTice Read each quesTion carefully Provide only one clearly indicaTed answer To each quesTion If your answer is illegible iT will be graded as incorrecT Show all work This porTion is 55 1 Angle Homes Real EsTaTe39 recenle began business in a cerTain ciTy They expecT Their firsT year39s profiT To be 38 Thousand dollars and for Their profiT To decrease by 007 Thousand dollars each year over The nexT 8 years The company plans To conTinuously invesT Their profiT inTo an accounT ThaT offers 37 APR compound conTinuously a DeTermine The income sTream funcTion RT Include uniTs b WhaT is The 8year fuTure value of This invesTmenT Show your work and include uniTs c CounTry Homes39 is inTeresTed in purchasing The Angel Homes Real EsTaTe39 Based on The 8year ouTlook whaT is The minimum amounT of money ThaT Angel Homes Real EsTaTe39 should accepT Show your work and include uniTs Page I8 Fall 2008 SecTions 55 amp 61 63 UniT 2 PracTice 2 Suppose overall demand for kerosene in The UniTed STaTes is given by Dp 15a 3 15 million gallons where p is The price per gallon in dollars Check poinT D51512 a WriTe an expression in Terms of pfor The elasTiciTy of demand 7 Don39T jusT wriTe The formula You musT show specific expressions for Dp and D39a for crediT b Find 7 when The price of kerosene is 349 per gallon Is demand for kerosene elasTic inelasTic or uniT elasTic aT This price Briefly explain The criTeria used To reach your conclusion c For whaT range of prices is demand for kerosene elasTic Page I9 Fall 2008 3 4 thousand rickets Page SecTions 55 amp 61 63 UniT 2 Pr39acTice Assume ThaT Clemson decides To sell all TickeTs To The 2008 home fooTball game againsT USC for a price of p per39 TickeT The supply and demand funcTions are given below 013 77 o when7 2 5 when7 lt 5 sltpgtl Thousand TickeTs supplied Dp 11563O95p Thousand TickeTs demanded 5 DIP Check poinTs eon D302481868027 400 200 5p 00 5 20 4O 60 80 p daarsper39 ticker a Find The consumer39 sur39plus when The price is 55 per39 TickeT Use The algebraic meThod and show all necessary sTeps Give your final answer39 as a decimal value 6395 J11563095pdp 55 CS include uniTs b Find The producers39 willingness and abiliTy To receive when The TickeT price is 30 Include uniTs 10 Fall 2008 C P SecTions 55 amp 61 63 UniT 2 PracTice WhaT is The TickeT price aT markeT equilibrium Include uniTs How many TickeTs will be sold aT equilibrium Include uniTs Shade The region on The graph below ThaT represenTs ToTal Social Gain aT markeT equilibrium Use The specific values for The equilibrium poinT you found above To wriTe The maThemaTical noTaTion for ToTal Social Gain aT markeT equilibrium Include uniTs You do noT have To compleTe The calculaTion NoTaTion 1000 u g 80 Vuth s u E 600 UnITs E x b 400 200 7 50gt a 0 5 20 40 60 80 p dolar39s per ticker Page I11 Fall 2008 Sections 55 amp 61 63 Unit 2 Practice 4 The amount of federal funding for student financial aid between 1980 and 2000 is given by fx 9032x2 9997x 36459 million dollars where x is the number of years after 1980 Check f5 437155 a Find the average amount of federal funding for student financial aid between 1983 and 2000 Show the mathematical notation that leads to your answer Include units b Find the average rate of change of the amount of federal funding for student financial aid between 1983 and 2000 Show the mathematical notation that leads to your answer Include units Page I12

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