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Pretest1Solutions - SOLUT/oA/s MATH 122 PRETEST 1 ° I This...

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Unformatted text preview: ' SOLUT/oA/s MATH 122 PRETEST 1 ° I This test is designed to give an example of what types of questions may be on the test. Show all work for full credit. ' 1. The average weight in pounds of American men in their sixties (in 1979) as a function of their heights in inches is given in the following table. “Hymn- a. How do you know from the )table that weight w is a linear function of height h? 31/156 M? haw égmllul Spaca/ h [/0]de we Can 15” 711,,‘5 ’ /5 4 linear #Mohm [47 "Ohm/lg the +5 ado/tho?! Path/A M 7%: w Values C1106 Ca)\0l also "Check gr 4 CbASIS/fll)’ 610,06) b. What is the slope of the function? (Be sure to give units of measurement as part of your answer.) Ah MM 0. Explain the meaning of the slope 1n terms of heights and weights. Er flmmca/z M64 [/2 flit/r axhrs [m I777) gawk add/Awal , Inc/n 0/) ire/fill} (“b/VCSflo/Ic/s h; an avg/Mm: 5 FM'OI5 of . 1. Weigh}. (:1. Find a formula that expresses the weight w in terms of the height h. W’lbé= 5(14-(08) w ’ Ila/a :51) - 340 2 2. Complete the table of values for the linear function. I. "la—n +9, Write the equation of this linear function. 3. Complete the table of values for the exponential function --n___ ' --”—m X/. (0 Write the equation of this exponential function. /0=/Zelm 7/382; . 0436 p a: 36 m) K64L [Brigg ZS [,4 Mafia P=[o.25€0“3t 1900 K20/l86-Slm! ' 4. Suppose that y— — x2 + as — 5. Find the average rate of change of y with respect to at over the interval 3 < x < 6. New), ‘- 3 5. Find the equation of the linear function that passes through the points (3,12) and (6 48). WM = /Z yl/Z=/Z(X’3) {rs ‘ \f-IZs/Zx 23(0 6. Find the equation of the exponential function that passes through the points (3,12) and (6 48). ,‘llaZ MHZ/{3) 43 L/K £5350 {3) #89,;6 K“) /2 85K 3K _' 233 We M ____f/ 3E 02 3K: fl‘llaZé'SIv/ei 7. The total cost 0 of producing an sneakers is given by the: function _ - C(a: )=0019:2 —0.2$+2000. Find the average rate of change in the cost if prOduction is increased from x = 100 to x— — 150 Give units. ' ' also) — 6000) 3 1195'? 20m _ /50—/OO . ‘ 50 4 8. A furniture company charges a fixed amount'plus a charge for each pound that they move. A person who shipped 50 lbs of furniture was charged $300 while someone else was charged $780 to move 210 lbs. ‘ ' ' ' ' ' ' a. Write a function that represents the moving cost, C, in terms‘of pounds, x. I ‘ Ms Ag : 7&9-300 , C ,3oo=3(x-5¢)j _ N 20-50 ~ .Ci3OO=3X*’5O ' : jaws/mm, - I. b. Find the vertical intercept and interpret it in relation to the problem. (0'0 6:3(0)+/so v—/nmep+r_ ‘ 6:150 ’fle mpg/1v, Chat/663 a fixd mm M 16/50 am 1‘3 flon/WJ Ls movfcl. 9. A business discovers a linear relationship'between the number of shirts it Can I sell and the price per shirt. In particular, 12,000 shirts can be sold at $19 each, and 3,000 of the same shirts can be sold at $55 each. a. Write the number of shirts, S, as a function of the price, p, per shirt. MSAS z 3% gamma—25.04049). A —- . V ' ‘0 55 ’7- 5'—/2z>oo:-—250+L/7so . _ = deaths/5,10,,“ 5»: —z 51.04% 50 - - b. What are the units of the slope? Interpret the meaning of the slope in} everyday language. ' Wm m business-win sell 250 karat/+5 / gr Each $7 If mcreasas 7% [an of. c. Find the horizontal intercept and interpret itin relation to the problem. ' (p, O) 0 = jaw/@750 Mnkmpk 250/ =M075?) - ' Ala )0/3’“ 020 3% 7,0“ 5141/71, PW ~ . 7% bus/2255 MN 44474-56” W7 ' I slay-ks. f :_ . 5 10. In physics it is shown that the height 3 of a ball thrown Straight upward with ' an initial velocity of 80 feet per second from a rooftop 96 feet high is s_(t ) = —l6t2 + 80t + 96 Where t is the elapsed time that the ball 1s in the air. The ball misses the rooftop on ' the way down and eventually strikes the ground. a. When does the ball strike the ground? 0"“ “W ”’4’ 1 '. m Ian was 7% 3mm 0:751 5£'& O: (If 'é>[£+l) all)!“ l/’ ’5 7’1’I/DKM. f: (a 15:4 éénmihm negahyefime b. Calculate the average velocity of the ball for its whole trip to the grOund. Give units. 5/60) 5(0) 0 % fl ————é= ’0 Z— - 111%“ 11. A population is growing according to the function _P = 250(1065)‘, where P is ‘ the population at year t. , , ' a. What is the initial population? [I’ll b. What is the annual growth rate? was : I+r r=0.0(os 1.- c. What is the population in 10 years? Pao) = 25o (1.0%)“) P00) :24109. 28% panel ; d. How many years will it take for t e population to reach 1000‘? 1000 = Zso(/.0(p6>t I 1/ =//11 0&5’5 mg ém “- 6 12. Suppose an account earns interest at an annual rate of 9%, compounded continuously. Determine the amount of money grandparents must set aside at the birth of their grandchild if they Wish to have $20,000 by the grandchild’s eighteenth birthday. nger'é 20m: POW) 6 0.0908) . W) # # 13. Money deposited in a certain bank account doubles every 13 years. If the bank compounds interest continuously, what annual interest rate does the bank offer? Aeé 8:100 zoouoogK/B) )n Z 3 1/18 BF IE 7‘5 144905332 4-5332; 1 14. A bakery has 250 lbs of flour. If they use 12% of the available. flour each day, how much do they have after one week? Write a formula for the amount of flour they! ' . . '- have left after t days. , . l73250(l#0.12) ’ one week- 3 75/m15 P= 250 0387* ’ 'P=‘Zoo(o.88)7 fox/(9‘7 its ofl flax ' at Her mc'weckye. 15. My husband and I have decided to start a muffin company, sanders’ Muffins. We do some research and find that we can rent a building for $1200 per month and 7. equipment for $375 per month, but we must Sign a contract that even if We make no muffins, we are responsible for these rental fees. We buy our ingredients in bulk, so . v l we spend about $0. 40 per muflin for ingredients. We decide to sell our muffins fOr'l; " $1. 50 apiece. . a. What is our cost equation 0, in terms of muffins, m? - C = /Zoo +395 man/n ; 5' ; 575 +0.40," b. What is the revenue equation, R, in terms of muffins, m? c. What is the profit equation, H, in terms of muffins, m? 7r: [50m - (/5625 fat/Om) d. How many muffins do we have to sell to make a profit? [50/14:]5751'0HOM fi llOmr’/575 :0, MOM : 1575 0 ' I 10m: 1595 WI 3 Hmeum/ts R l ' im [650de M”: gMaK’evé’I) pom We have +72 sen 4+ Ima_ +5 mane {W45 8 16. The figure below gives both supply and demand curves for a certain economic good. . p @ficehldnlhrsiiinm) "mi 1" ‘fikgflé’qx—fl‘ :VpSfihfii :0. V1.3 1060‘ 1.2fifi0“ 1.3000_.HW,400n1.g 5000 a. Why is the supply curve increasing as 'you move to the right? l 716 pace [/16me (4051.17 H16 @pr 1s Marmot. _ _ . SUPPLCV5 and Marc NIH/31p produce when 119 lance (514151: b If the price is $50 per item, the producers will supply £91. items c. Why 18 the demand curve decreasing as you move to the right? I 71%, ,che 616611901665 (hash/:3 Ht 91914611401 1‘0 MW (answers am: more refill/13 ‘1'0 by} when 114:,- ,oncc ,5 1010 d. If the price is $50 per item, the consumers will buy M— items e. If the price is $50 per item, what would you predict about the future price of the . good? Explain. A161 pHCC’ 0p $60/ SUPPH €XC€€OIS demand (ham/)8.“ 4 “Surglds, . fly; 741m pace 5140le be - _ . 9 17. What interest rate, compounded annually, is equivalent to a 7% rate com- pounded continuously? ; 0,04 ‘ 4:6 446 a: /,07Z5/ |+r2 L0725l r: 0.01251 <4 725] mel 18. What interest rate, compounded continuously, is equivalent to a 7% rate com- pounded annually? p K we I. 0? ’ 6 M [107): Me - . 0.0027(00— K 6' 5 :Maéz Conimoaas 19. If you invest your money in an account paying 4% interest per year, com— .. pounded annually, how long will it take for your money to double? let IZ=/oo zoo 1000043 [“2 lnlflOLl ‘an: 15W ’9 ‘L; M000 hflafls 20. If 250mg of a radioactive element decays to 200mg in 48 hours, find the half— life of the element. 200,250 ([483 . . 15g 3:109 ’10. Wat " fist ‘ I ‘ ' 50-: mag Lw28,Mg , «oaflwb Mos) : 48K to 5: M6 77? 71? '10 21. A bird species in danger of extinctiOn has a population that is decreasing , exponentially. In the year 2000 the population was 1400, but by 2005, the pOpulation was only 1000. Once the population drops to 100, the situation Will be irreversible. When will this happen? . K(5 > _‘ ~0.0lo73£ _' £55 2051) 106 £50 ‘ [oops/40085; / iO=/Ll/OO€ 0'Ob73‘g 7%” 2005 .3. (75 ' 1.4 (5/7)?)05 .1 ’ lfl(_//L/>:/ 46 ,. p In (5/?) 15/5 ' . [/1 (VP!) 1: fWi 14: «2.01073 75361.21? W5 ‘ 55,,” . m 5.4mm to.“ be woe/mm m I:21.nabinT;1f:elr1a5lg-lglfecfa‘lcfi)sf?c:es1um—137 1s 30 years. How much of a 100-mg sample would ' m [61 $4001 SDI/006:?) ?= [DOG '0025\(§-_O> ["015 :1” 6. . P: g/Hqgm . M06 = 221.219 . “3'6- 3‘9 K :. ’0. 0231 25m. I 23. Bank A offers 12% interest, compounded annually, and bank B offers 11.8% interest, compounded continuously. You want to invest $1000 for 10 years. Which bank should you choose? Show your computations. W W . lo 0.I\8(I0) P2100000) P; 10006 . ' P353105 85 ' P $5254 5? mo 5%)” Chooseg m 24. 25.f 26. 11 Solve for x. 3(4“+2)— 7= 8 34V“)4 WIL’Xi'Z IA: /5 . ., w W 73-7, .. X+Z HM —. (gFor )(xf —— —2m2 — 22: and g(x )— — 33: -.— 1, findand'simplify each of thé following. 2P(5x 43 2 ‘ 2(3X 152' 2(5x-I3 — :‘ZZMX ’3x'3x+|)’-[0>‘*Z I ' ' 8x «(ax Hafiz M151: 32‘ "82”” - g(f(a:)) = 9(sz —2x) ' ' ’ i ‘ :3ax,&>4 A '— Use the following table to find each of the following. “In“ -”-I --ll-n 12 27. The frequency, F, of a vibrating string is directly proportional to the square root of tension, t. If a string vibrates at a frequency of 144 hertz due to a tension of 2 pounds, find the frequency when the tension is 18 pounds. F: K1? ' :10182310? WI: 141/7 . F: 1011823177977 ‘ W” W F:_m 28. Intensity of illumination from a light source is inversely proportional to the square of the distance from the source. If the intensity of a light source is 100 lumens . _ _ . at a distance of 20 feet, find the intensity at 30 feet. ...
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