Math 105 Second Midterm March 16, 2017

Transcription

1 Mah 105 Second Miderm March 16, 2017 UMID: Insrucor: Iniials: Secion: 1. Do no open his exam unil you are old o do so. 2. Do no wrie your name anywhere on his exam. 3. This exam has 9 pages including his cover. There are 9 problems. Noe ha he problems are no of equal difficuly, so you may wan o skip over and reurn o a problem on which you are suck. 4. Do no separae he pages of his exam. If hey do become separaed, wrie your UMID on every page and poin his ou o your insrucor when you hand in he exam. 5. Please read he insrucions for each individual problem carefully. One of he skills being esed on his exam is your abiliy o inerpre mahemaical quesions, so insrucors will no answer quesions abou exam problems during he exam. 6. Show an appropriae amoun of work (including appropriae explanaion) for each problem so ha graders can see no only your answer, bu also how you obained i. Include unis in your answer where ha is appropriae. 7. You may use a TI-84, TI-89, TI-Nspire or oher approved calculaor. However, you mus show work for any calculaion which we have learned how o do in his course. 8. If you use graphs or ables o find an answer, be sure o include an explanaion and skech of he graph, and o wrie ou he enries of he able ha you use. 9. Turn off all cell phones, pagers, and smarwaches, and remove all headphones. Problem Poins Score Toal 100

2 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 2 1. [15 poins] a. [5 poins] Suppose f(x) is a funcion wih domain [ 2, 5] and range [7, 12]. Wha are he domain and range of he ransformaion g(x) = f(2x + 1) + 2? The domain of g(x) is. The range of g(x) is. b. [4 poins] Suppose y = p() has verical asympoe = 1 and horizonal asympoe y = 2. Give he equaions for a horizonal and verical asympoe of he funcion y = 2p( + 3) + 1. A horizonal asympoe of 2p( + 3) + 1 is. A verical asympoe of 2p( + 3) + 1 is. c. [6 poins] A graph of he funcion h() is given below. On he empy se of axes, carefully skech a well-labeled graph of j() = 1 2h( + 2) 1. 4 h() 4 j()

3 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 3 2. [11 poins] The number of bees on Percy s uncle s farm has been decreasing over he pas five years. The number of bees years afer 2012 on he farm is given by he exponenial funcion B() = 7000e 0.2. a. [3 poins] Find he annual decay rae of he bee populaion in exac form. The annual decay rae is. b. [4 poins] Percy s uncle will need o order more bees when he populaion of bees falls below How many years afer 2012 will his occur? Give your answer in exac form or accurae o hree decimal places. Percy s uncle will need o order more bees years afer c. [4 poins] The number of mosquioes on Percy s uncle s farm has been increasing a an annual rae of 9%. Find he doubling ime of he mosquio populaion. Give your answer in exac form or accurae o hree decimal places. The doubling ime of he mosquio populaion is years.

4 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 4 3. [17 poins] a. [4 poins] Circle all graphs in which he graphed funcion appears o be periodic wih more han one period shown. b. [2 poins] Find he period of he funcion in he following graph: The period is. c. [5 poins] Find he midline and ampliude of he funcion graphed in b. The midline is. The ampliude is. For pars d. and e. suppose C() is he oal number of calls received by a call cener hours afer 8:00am on a normal day. Each senence describes he number of calls he cener receives on a paricular day; circle he expression ha corresponds o he given descripion. d. [3 poins] The call cener received 20 more calls han normal righ a he beginning of he day, bu oherwise i was a normal day. C() + 20 C( + 20) 20C() C(20) None of hese e. [3 poins] The cener was closed unil noon, and a all imes during he afernoon he call volume was wice wha i normally would have been 4 hours earlier. 2C( + 4) C(2 + 8) C(2 + 4) 2C( 4) None of hese

5 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 5 4. [11 poins] In chemisry, he ph of a subsance is a funcion of he concenraion of hydrogen ions per lier of he subsance. The ph of a subsance wih concenraion C hydrogen ions per lier is A(C) = log(c). a. [2 poins] Lemon juice has a ph of Wha is he concenraion of hydrogen ions per lier of lemon juice? Give your answer in exac form. The concenraion of hydrogen ions in lemon juice is ions per lier. b. [4 poins] If he number of hydrogen ions per lier C in a subsance is doubled, wha is he resuling change in ph? Wrie increases or decreases in he firs blank, and he amoun of increase or decrease in he second blank. Give your answer in exac form. When he concenraion of hydrogen ions in a subsance doubles, he ph by. c. [2 poins] The owner of he Peer and Sarah s regular pizza place is looking ino canning her pizza sauce o sell in he supermarke. Currenly her sauce has hydrogen ions per lier. Wha is he ph of her sauce? Give your answer in exac form or accurae o hree decimal places. The ph of he sauce is. d. [3 poins] The sae healh deparmen requires ha he sauce have a ph lower han 4.7 in order for he sauce o be canned. How many imes as many hydrogen ions per lier (compared o he curren ) will he sauce need in order for he healh deparmen o allow i o be canned? Give a whole number answer ha resuls in a ph above 4 and below 4.7. The sauce needs imes as many ions per lier o be canned.

6 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 6 5. [8 poins] Percy is building a zipline from he roof of his uncle s barn o he base of he farmhouse. The roof of he barn is 20 fee off of he ground. Looking a a 32 degree angle above he ground, he can see he roof of he farmhouse from he ground a he base of he barn. The line from he roof of he barn o he base of he farmhouse makes a 53 degree angle wih he side of he barn. The siuaion is picured below. 20 f 53 o R H 32 o a. [3 poins] Find R, he disance from he roof of he barn o he base of he farmhouse. Express your answer in exac form. R =. b. [5 poins] Find H, he heigh of he farmhouse. Express your answer in exac form. (Hin: You may wan o find he disance beween he bases of he buildings firs) H =.

7 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 7 6. [15 poins] A he park, Prem is riding on a merry-go-round of radius 6 fee spinning a a consan speed, and Peer is waching, 7 fee away from he merry-go-round. Prem sars a he poin A and afer 1.5 seconds he s a he poin B. The siuaion is depiced below. The moion of he merry-go-round is couner-clockwise. B 120 o A Peer 3 fee 6 fee 7 fee a. [2 poins] How long does i ake for he merry-go-round o complee one revoluion? I akes he merry-go-round seconds o complee one revoluion. b. [2 poins] How far did Prem ravel along he circumference of he merry-go-round beween poin A and poin B? Give your answer in exac form. Prem raveled fee beween poin A and poin B. c. [2 poins] By how many radians does he merry-go-round roae in 3 seconds? Give your answer in exac form. The merry-go-round roaes radians in 3 seconds. d. [3 poins] Find he disance beween Peer and he poin B. The disance beween Peer and he poin B is fee. e. [6 poins] Find a funcion D(θ) ha gives he disance in fee beween Prem and Peer afer Prem has roaed θ degrees from he poin A. D(θ) =.

8 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 8 7. [8 poins] A Peer and Sarah s regular pizza place, he pizza is 50 degrees Fahrenhei when i goes ino he oven. The oven is 800 degrees Fahrenhei, so a pizza lef in he oven will reach 800 degrees afer a long ime. Afer 6 minues in he oven, he pizza is 200 degrees. The emperaure of he pizza in degrees Fahrenhei afer minues in he oven is a funcion of he form P () = A + Be k wih k < 0. Find he values of A, B and k in exac form. Show all of your work. A = B = k = 8. [7 poins] The emperaure in degrees Fahrenhei of he lasagna a he pizza place minues afer i comes ou of he oven is L() = (0.9). a. [2 poins] Wha is he air emperaure in he pizza place? The air emperaure in he pizza place is b. [2 poins] Wha is he emperaure of he lasagna immediaely afer i comes ou of he oven? The emperaure of he lasagna immediaely afer i comes ou of he oven is c. [3 poins] How long afer he lasagna comes ou of he oven does i reach perfec eaing emperaure of 150 degrees Fahrenhei? Give your answer in exac form or accurae o hree decimal places. The lasagna reaches 150 degrees minues afer i comes ou of he oven.

9 Mah 105 / Exam 2 (March 16, 2017) DO NOT WRITE YOUR NAME ON THIS PAGE page 9 9. [8 poins] The following able gives values of several funcions a differen poins. Use he able o answer he quesions below X() Y () Z() a. [2 poins] Could X() be an odd funcion or an even funcion or can you be sure i s neiher even nor odd? Circle your answer. could be even could be odd couldn be even or odd b. [6 poins] Which of he following ransformaions of X() could be Y (), and which could be Z()? Wrie he leer(s) corresponding o your answers in he space provided. There could be more han one answer for each blank. 1 (A) 2X(3 + 3) 2 (B) 2X( 1 3 ) + 1 (C) X( + 3) (D) X( 1) 1 Y () could be. Z() could be.