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# MAT119 M4WA4

AU

GPA 3.8

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Date Created: 11/15/15

Written Assignment 4 SECTION 36 2 gX 5x6 3 2 Exercise 2 1 5 gX 506 0 gX 5 16 5 gX 526 32 1 0 5 gX 516 5 gX 5 26 32 2 3 2 fx x3 4x3 3x 8 Exercise 10 Graph C Highest degree is 3 since it is odd end behavior will result in opposite directions and the leading coefficient is negative which will have that rise than fall Y intercept of this polynomial 8 fX X54X4X3 16X212X5 Exercise 14 Graph A Highest degree is 5 with a negative leading coefficient Which gives you a graph that that has a rise and fall line starting this also Will have more dips in the graph compared to the other graphs since there are more degrees Y intercept is 5 f x x 5X 1X 1 Exercise 16 f 0 0 50 10 1 f 0 511 f 0 5 YIntercept 5 fx 050101 0 x5l l These are where the graph crosses the xaxis Exercise 34 Yea 199 1995 200 200 2004 2006 r 0 0 3 Sale 856 1059 916 965 1047 1101 5 3 4 0 5 2 5 23x32 8000SySl2000 A Plot points with X 0 2000 In the viewing Window and Entered Year into L1 and sales into L2 B Use cubic regression to find a 3rd degree polynomial function gX that models this data gx 571x3 13734x2 89958x860861 Written Assignment 4 C Graph gX on the same screen as the data does this fit well Yes this does fit this data well D Estimate Lottery Sales in 2005 Estimated sales for 2005 are 10472 when using the cubic regression function as stated in B if estimated the sales based upon the points given sales would fall between 10472 and 11015 E Why is this going to be inaccurate beyond 2007 It is inconsistent and an unpredictable trend of data without any predictable progressionregression SECTION 37 Exercise 2 x 60 0x 7 y Bx 6 1 H O x Vertical Asymptote Horizontal Asymptote x 2 gx Exercise 6 Vertical Asymptote Horizontal Asymptote x2 X g x21 Exercise 18 x2 10 x221 x 1 Vertical Asymptote Horizontal Asymptote Since the degree of the numerator is lt the degree of the denominator the y 0 HA is 900 000 000 30 000x x 90 000 Exercise 27 When X 0 you are given the y intercept which is also the max number of blue tranquilizers 10000 900000000 30 0000 900 000 000 0 90 000 90 000 10 000 Written Assignment 4 To solve for the max number of red tranquilizers produced set y 0 and solve 900 000 000 30 000x x 90 000 900 000 000 30 000x x 90 000 0 30 000x 900 000 000 30 000x 30 000x 30000x 900000000 30 000 30 000 x 30000 0 x 90 0000 2 x 90 000 Cx 2x3 25x2 1 531x 25 000 Exercise 31 Produce no more than 110 units how many units should be produced to have lowest avg cost To have the lowest cost 739 units should be produced This is the minimum point on the graph Which is found when inputting the function below which gives the average price function Tracing the point along the line in the calculator will give you the lowest point Cx 2x3 25x2 1 531x 25 000 3 2 CX CX 2x 25x l53lx25 000 x x Ex 2x2 25x1531M x SECTION 41 Classify as linear quadratic 0r exponential gx 5x ymxb Exercise 2 Linear since it follows kx 4quot3 Exercise 4 Exponential since the variable is raised to the exponent kx 53 Exercise 10 A Describe shape of graph without graphing This will remain above the X axis since a gt 1 it will increase drastically once it crosses the y intercept since the variable is in the exponent as long as it continues to increase positively When the variable becomes negative it will become a smaller number but will never reach 0 Written Assignment 4 B Find 2rld coordinates of the points with the 1st coordinates 0 and l k0 530 51 5 Gives the point 0 5 k1 531 53 15 Gives the point 1 15 Exercise 20 Graph these on the same axes fX3quot fx3quot2 fX3x4 A B C fX3x2 fX3x fX3x4 will have a y intercept 2 points above and will have a y fX3x fX3x 4 fX3x intercept 4 less than is the only function with a X intercept will fx 3x 2 reach the X axis but never fall below while will never touch the X axis y3xc y3x c D If c is a positive constant explain how the graphs of and are related to A y 3x c It would have a different yintercept either moving the graph up the y axis for or down y 3x c the y axis for x a 41 a Exercise 24 When xltl but xgt0 the majority of the line will be to the left of the y axis Line D falls in the middle of two other lines with similar characteristics possible answers are 753l and 41 the best choice for x in this case is 41 x a 32 a Exercise 26 for line F This is the largest possible answer and has the greatest increase and lies to the right side of the y axis f x ax Exercise 30 Give a rule of the form to determine exponential function whose graph contains the given point f 3 61 3 64 61 3 8 3 3 a 64 8 23 27 A 38 B 364 Written Assignment 4 y1 03 97 Exercise 36 Money loses value at a rate of 3 per year the value of 1 in tyears is given by A t 0 1 2 3 4 5 6 7 8 9 10 y 1 97 94 91 89 86 83 81 78 76 74 10 y971y972 y97 y97 y94 y74 s c1 rquot Exercise 42 Determine scrap value of machine at end of useful life C 68000 Original cost 10 years useful life 8 annual rate of loss 8 680001 810 680001 0810 68 000 92 68 000434 29 53841 gx 788 gtlt1112quot Exercise 46 g9788gtlt11129 788 2599 048012 Billions of dollars g10788gtlt11121 788 28909 27810685 Billions of dollars By the year 2013 or g 13 there will be approx 31325 billion dollars spent SECTION 42 4624 h0gtlt1065 4624 ho XI 4624 ho X1 H8 4624 gtlt10658 H10 4624 gtlt106510 H12 4624 gtlt106512 1 1 H8 4624 gtlt1655 H10 4624 gtlt1877 H12 4624 gtlt2129 4624 ho H8 765272 H10 867925 H12 984450 Exercise 2 A B f50 353 x1950 50 353 x1950 f0 353 gt490 353 353 f14 353gtlt100714 f30 353gtlt100730 f0 353gtlt1 50 950 1007 f14 353gtlt1103 f30 353gtlt1233 f0 353 3537 39 f14 38936 f30 43525 Exercise 6 A C The AA population should reach 55 million by the year 2064 Written Assignment 4 f28 3505 gt628 25356 3505gtlt1928 f 0 3505gtltIa0 3505 3505 f33 3505gtlt107333 f36 3505gtlt107336 f0 3505gtlt1 A 1 28 928 1 073 f33 3505gtlt10228 f36 3505gtlt12635 f0 3505 35057 39 f33 35849 f36 44286 Exercise 12 A B C Consumer credit will reach 6000 Billion in the year 2053 Wt 60 30 65 Exercise 14 W0 60 30 6750 W1 60 30 6395 1 W4 60 30 6 5 W6 60 30 63956 W060 301 30 W1 60 306395 W4 60 306392 W6 60 306 3 A B C D 0 800 6 314 0 12 908 4 18 157 62 pa 20 000 24 188 1 24 2 3 65 Exercise 20 30 197 34 p0 w 36 199 1 24 2 36 40 20 000 42 199 p01242 87 20 000 48 199 190 1 241 97 p0 20 200 800 The population grew the most within the rst yeah Written Assignment 4 SECTION 43 log 001 3 10 3 i3 L 001 10 1000 Exercise 6 632189 Exercise 10 4 1 1 L0g0001 4 gt 10 4 0001 10 10000 Exercise 14 L0 i3 3 i127 037 83 27 33 39 Exercise 20 L0g20 L0g5 Log 13010 1861 Exercise 30 Ln3x 2 Lnx 4 Ln3 X 2X 4 Ln3 X2 14 X 8 Exercise 36 L0g5 06989 L0g5x2 y3 2 Log Sxy Log xy Logy Exercise 38 L Log6 60 L0g606 0g6 60 L0g606 Exercise 50 T 143Ln w 4998 n Exercise 62 T 443M 10000 5001 4998 500 7 T 143Ln 24990007 T 143Ln 003801 T 7969 a b T 443M 10000 10001 4998 5000 7 T 143Ln w 24 990 0007 T 143Ln 00020008 T 12179 SECTION 44 Written Assignment 4 1n8k 7 1n34k ln 1113 1n8k 7 1n34k 117 34k 8k 7 Ll 8k 7 245 327k 34kjk 9 1 17 2E 34k 8k 327k 7 245 327k 327k 473k 772457 473k 945 473 473 k945 473 Ekar eZ h 5x2 zm4h x3 5x2 x 5x24x12 5x2 24x12 2 5x 4x4x 4x10 x10 Ekare4 L0g53x 4 1 Ekare8 3x 4 3x 4454 3x9 3x 9 3 L0g53gtlt3 4 1 x3 L0g551gt515 1n2x1 11nx 2 2x1 1n52 1n41n13 1n521n413 1n52 1n52 x 2 1n2gtlt 2 1 1 1n2 2 1 2xx 2 1n 41 11n 4 2x xxx2 ln 5 11n4 x 2 lIl 4 ln4 Exercise 14 x11 x21 10gx 110gx21 x 1111 x2212 x1x21 x2 x 1 Exercise 16 log1 log4 1 10g 14 1 Exercise 24 Exercise 28 Exercise 36 Exercise 46 Written Assignment 4 log2 1log221 log 2log11 Nonreal answers 16 x28 24 x2 23 4x83 4x8 83 8 4x 5 1 1 x 5125 Ln16quot Ln64 an16 Ln64 x Ln64 1 5 16quot 64 Ln16 39 43x 1 3x 2 Ln 43 Ln 3 3x 1ln4x 2ln3 3xln4 1ln4 xln3 2ln3 3x1n4 xln3 11n4 11n4 11n4 2ln3 3x1n4 xln3 11n4 2ln3 31n4ln3x11n4 2ln3 31n4ln3 x11n4 2ln3 31n4ln3 TL3ln4lnBJ log4z3 log4z 3 2 log453log45 3 2 log48log42 2 10g4822 z 32 Z32 log4162gt4216 z 3323 Z3323 z5 z 1 Written Assignment 4 32quot 228 2 x21n3ln8 2 x21n3 ln8 1113 E kw 1099 2 x21892 2 x2x2l892x2 21892x2 2 18921892 1892x2 10812 i 108x Exercise 58 fx 104gtlt1024x Exercise 64 l6trilli0n 104 gtlt1024x 16 104gtlt1024x 104 104 40249 104 In 3 1047 11111024 1111024 1111024 In 116 43078 0394 139 21817 1111024 02372 A In the year 2018 the GDP will reach 16 Trillion B In the year 2044 the GDP will reach 30 Trillion 30trilli0n 104gtlt1024x 30 104gtlt1024x 104 104 40241 104 In E 1047 11111024 1111024 1111024 In 130 10594 0394 1 39 24467 1111024 02372

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