Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition

,16758&725 $16:(56 ),1,7(0$7+(0$7,&6)25 %86,1(66(&2120,&6/,)(6&,(1&(6 $1’62&,$/6&,(1&(6 )2857((17+(‘,7,21 5DPRQG%DUQHWW Merritt College 0LFKDHO=LHJOHU Marquette University .DUO%OHHQ Marquette University &KULVWRSKHU-6WRFNHU Marquette University 7KHDXWKRUDQGSXEOLVKHURIWKLVERRNKDYHXVHGWKHLUEHVWHIIRUWVLQSUHSDULQJWKLVERRN7KHVHHIIRUWV LQFOXGHWKHGHYHORSPHQWUHVHDUFKDQGWHVWLQJRIWKHWKHRULHVDQGSURJUDPVWRGHWHUPLQHWKHLU HIIHFWLYHQHVV7KHDXWKRUDQGSXEOLVKHUPDNHQRZDUUDQWRIDQNLQGH[SUHVVHGRULPSOLHGZLWKUHJDUG WRWKHVHSURJUDPVRUWKHGRFXPHQWDWLRQFRQWDLQHGLQWKLVERRN7KHDXWKRUDQGSXEOLVKHUVKDOOQRWEH OLDEOHLQDQHYHQWIRULQFLGHQWDORUFRQVHTXHQWLDOGDPDJHVLQFRQQHFWLRQZLWKRUDULVLQJRXWRIWKH IXUQLVKLQJSHUIRUPDQFHRUXVHRIWKHVHSURJUDPV &RSULJKW‹E3HDUVRQ(GXFDWLRQ,QF $OOULJKWVUHVHUYHG1RSDUWRIWKLVSXEOLFDWLRQPDEHUHSURGXFHGVWRUHGLQDUHWULHYDOVVWHPRU WUDQVPLWWHGLQDQIRUPRUEDQPHDQVHOHFWURQLFPHFKDQLFDOSKRWRFRSLQJUHFRUGLQJRURWKHUZLVH ZLWKRXWWKHSULRUZULWWHQSHUPLVVLRQRIWKHSXEOLVKHU ,6%1 ,6%1 ANSWERS Diagnostic Prerequisite Test Section references are provided in parentheses following each answer to guide students to the specific content in the book where they can find help or remediation. 1. (A) (y + z)x (B) (2 + x) + y (C) 2x + 3x (A.1) 2. x3 – 3×2 + 4x + 8 (A.2) 3. x3 + 3×2 – 2x + 12 (A.2) 4. – 3×5 + 2×3 – 24×2 + 16 (A.2) 5. (A) 1 (B) 1 (C) 2 (D) 3 (A.2) 6. (A) 3 (B) 1 (C) – 3 (D) 1 (A.2) 7. 14×2 – 30x (A.2) 8. 6×2 – 5xy – 4y 2 (A.2) 9. 1x + 221x + 52 (A.3) 10. x1x + 321x – 52 (A.3) 11. 7>20 (A.1) 12. 0.875 (A.1) 13. (A) 4.065 * 1012 (B) 7.3 * 10 -3 (A.5) 14. (A) 255,000,000 (B) 0,000 406 (A.5) 15. (A) T (B) F (A.1) 16. 0 and – 3 are two examples of infinitely many. (A.1) 17. 6x5y 15 (A.5) 18. 3u4 >v2 (A.5) 19. 6 * 102 (A.5) 20. x6/y 4 (A.5) 21. u7>3 (A.6) 22. 3a2 >b (A.6) 23. 59 (A.5) 24. x + 2×1>2y 1>2 + y (A.6) y5 25. a 2 + b2 (A.4) ab 26. a 2 – c2 abc xy 1 -1 (A.4) 28. 2 (A.4) 29. (A.4) 30. (A.6) x 7(7 + h) y-x xy 31. (A) Subtraction (B) Commutative ( + ) (C) Distributive (D) Associative ( # ) (E) Negatives (F) Identity ( + ) (A.1) 32. (A) 6 (B) 0 (A.1) 33. 4x = x – 4; x = – 4>3 (1.1) 34. – 15>7 (1-2) 35. (4/7, 0) (1.2) 36. (0, – 4) (1-2) 37. x = 0, 5 (A.7) 38. x = { 17 (A.7) 39. x = – 4, 5 (A.7) 40. x = 1, 16 (A.7) (A.4) 27. Copyright © Pearson Education, Inc. A-1 ANSWERS Chapter 1 Exercises 1.1 1. x = 5 2. x = – 9 3. x = 2 4. x = – 3 5. x = – 19 6. x = – 2 7. 4 … x 6 13 8. – 3 6 x … 5 9. – 2 6 x 6 7 10. – 6 … x … – 1 11. x … 4 12. x Ú 9 13. 1 – 8, 24 14. 3 – 1, 52 3 15. 1 – ∞, 92 16. 34, ∞ 2 17. 1 – 7, – 54 18. 3 – 3, 22 19. x = 2 15 10 3 2 20. m = 14 21. y 6 22. x 7 23. u = 24. y = 2 3 4 3 27. y Ú 3 28. x … 8 29. x = 36 25. x = 10 26. x = 4 36 30. y = – 6 31. m 6 32. u 6 16 7 33. 3 … x 6 7 or 33, 72 x 3 34. – 2 … x 6 3 or 3 – 2, 32 36. – 9 … t … 9 or 3 – 9, 94 3 x – 3 4 22 22 1 14 3 6 220 9 32. x 20 5 x 33. y 5 y 5 y 5 34. x53 y52 y 5 22 x 5 23 y – b 35. – 4 41. 36. 5 3 37. 5 (A) 42. y 10 (C) 2 38. 3 39. 2 (C) y (A) (B) 1 40. 8 43. y 3,000 6 (B) 10 x 10 x 45. Negative 46. Positive 5 x 5 x 5 x 3 y + 12 2 40. m = x 9 42. F = C + 32 43. – 2 6 x … 1 or 1 – 2, 14 5 14 14 x 44. … u … 6 or c , 6 d 3 3 u 5 x t 47. 4,500 $35 100 x tickets and 5,000 $55 tickets 48. 30 quarters; 70 dimes 49. Fund A: $180,000; Fund B: $320,000 50. Fund A: $340,000; Fund B: $160,000 51. $15,405 52. $24,493 53. (A) $420 (B) $55 54. (A) $51 (B) $160 55. 34 rounds 56. 12 times 57. $32,000 58. (A) $20,000 (B) $24,493 (C) Choose the payment method with the larger base salary unless you can sell more than $52,000 per month. 59. 5,851 books 60. 7,132 books 61. (B) 6,180 books (C) At least $11.50 62. (B) 7,480 books (C) At least $15.60 63. 5,000 64. – 45 … C … -10 65. 12.6 yr 66. 9.6 to 16.8 2. (A) 44. 45. (A) y 5,000 4,000 3,000 2,000 1,000 0 20 3. (C) 4. (B) 5. y 5 6. (B) x int.: 3.5; y int.: – 4.2 y 10 10 x 60 100 x (C) 46. (A) 10 210 Exercises 1.2 1. (D) 5 5 x 39. y = – 1A>B2x + 1C>B2 = 1 – Ax + C2 >B 5 41. C = 1F – 322 9 5 x 3 29 38. x = – 5 7 35. – 20 … C … 20 or 3 – 20, 204 37. y = 2 1 1 1 ; y int. = 14. Slope = ; y int. = 4 3 5 2 15. Slope = 2; x int. = – 5 16. Slope = – 4; x int. = 3 17. Slope = 8; x int. = 5 18. Slope = – 3; x int. = 2 9 6 4 21. y = 2x + 1 19. Slope = ; x int. = – 7 20. Slope = – ; x int. = 7 2 9 6 9 1 22. y = x + 5 23. y = – x + 6 24. y = x 3 7 2 1 25. x int.: ; y int.: 1; y = – 2x + 1 26. x int.: 1; y int.: 3; y = – 3x + 3 2 x x + 1 28. x int.: 2; y int.: – 1; y = – 1 27. x int.: – 3; y int.:1; y = 3 2 y y y 29. 30. 31. 13. Slope = y 10 10 6 x y 5 210 5 x 5 x (D) x int.: 3.5; y int.: – 4.2 (B) x int.: 6.5; y int.: 5.2 7. 8. y 5 x 3 6 A-2 y 1 x 9. Slope = 5; y int. = – 7 10. Slope = 3; y int. = 2 5 11. Slope = – ; y int. = – 9 2 10 12. Slope = – ; y int. = 4 3 Copyright © Pearson Education, Inc. (C) (D) x int.: 6.5; y int.: 5.2 10 210 10 210 Answers 4,000 2,000 100 x 60 73. (A) R = 1.4C – 7 (B) $137 74. (A) R = 1.5C + 3 (B) $158 75. (A) V = – 7,500t + 157,000 (B) $112,000 (C) During the 12th year V (D) 76. (A) V = – 6,800t + 224,000 (B) $156,000 (C) During the 19th year (6, 112,000) $120,000 V (D) (11.6, 70,000) $80,000 $40,000 0 10 20 Years t $200,000 $160,000 $120,000 $80,000 $40,000 Dollars Demand 0 9,200 9,800 x Millions of Bushels Exercises 1.3 1. (A) w = 49 + 1.7h (B) The rate of change of weight with respect to height is 1.7 kg/in. (C) 55.8 kg (D) 5′6.5″ 2. (A) w = 52 + 1.9h (B) The rate of change of weight with respect to height is 1.9 in./kg. (C) 67.2 kg (D) 5′9.5″ 3. (A) P = 0.445d + 14.7 (B) The rate of change of pressure with respect to depth is 0.445lb/in.2 per ft. (C) 37 lb/in.2 (D) 99 ft 4. (A) P = 0.43d + 14.7 (B) The rate of change of pressure with respect to depth is 0.43 lb/in.2 per ft. (C) 36.3 lb/in.2 (D) 102 ft 5. (A) a = 2,880 – 24t (B) – 24 ft/sec (C) 24 ft/sec 6. (A) a = – 16t + 2,880 (B) – 16 ft/sec (C) 16 ft/sec 7. s = 0.6t + 331; the rate of change of the speed of sound with respect to temperature is 0.6 m/s per °C. 8. x = 3.9t + 1,403; the rate of change of the speed of sound with respect to temperature is 3.9 m/s per °C. (B) The rate of change of fossil fuel 9. (A) y production is – 0.19% per year. 100 80 (C) 76% of total production (D) 2058 10. (A) (10, 156,000) 11. (A) 10 20 Years t 0 10 20 x Thousands of Feet 225 215 205 195 185 (31, 227.4) 0 Dollars f 12. (A) 0 3 6 9 12 15 18 Years since 1997 (28.97, 199) 14. (A) 9.5 Demand 0 3,400 4,200 x m 25 20 15 10 5 0 3 6 9 12 15 18 Years since 1997 t (B) 2029 y (B) 1,050,000 (C) 1,359,000 (B) 6,428,000 (C) 10,339,000 1 0.5 0 0.5 1 Population (millio Supply 9 t (B) 2025 0 28 30 32 x Barometric Pressure (inHg) 10 5 10 15 20 25 30 x Years since 1985 25 20 15 10 5 13. (A) 79. (A) T = 70 – 3.6A (B) 10,000 ft 80. (A) T = 3.2A + 200 (B) 220.8 mph 81. (A) N = – 0.0063t + 2.76 (B) 2.45 persons 82. (A) I = 1,031t + 30,000 (B) $71,240 83. (A) f = – 0.49t + 21 (B) 2028 84. (A) m = – 0.6t + 25.7 (B) 2031 85. (A) p = 0.001x + 5.4 (B) p = – 0.001x + 13 (C) (3,800, 9.2) (D) Equilibrium point p (B) The rate of change of fossil fuel consumption is – 0.14% per year. (C) 81% (D) 2030 y 100 80 60 40 20 Licensed Drivers (millions) (3.5, 205.56) (6.522, 200) Temperature (8 F) Temperature (8F) 77. (A) T = – 1.84x + 212 (B) 205.56°F (C) 6,522 ft T 78. (A) T = 14x – 206.6 (B) 227.4°F (D) T 220 (C) 28.97 inHg (D) x 5 10 15 20 25 30 Years since 1985 (18.24, 100,000) 0 210 200 190 180 60 40 20 0 Female Smokers (%) 0 20 2.80 Male Smokers (%) (C) The y int., $1,905, is the fixed cost, and the slope, $39, is the cost per racket. 6,000 Supply (B) p = – 0.0005x + 7.8 (C) (9,500, 3.05) 2 87. (A) s = w (B) 8 in. (C) 9 lb 5 88. (A) d = – 4w + 30 (B) 30 in. (C) 7.5 lb 3.00 y 40 20 0 20 40 x Population (millions) 15. (A) Net Sales (millions) (B) Equilibrium point 3.20 U.S. Fossil Fuel Production (%) 72. (A) C = 39x + 1,905 x 50 100 150 p (D) Licensed Drivers (millions) 0 C 86. (A) p = 0.0005x – 1.7 U.S. Fossil Fuel Consumption (%) 47. x = 4, y = – 3 48. x = – 5; y = 6 49. x = – 1.5, y = – 3.5 50. x = 2.6; y = 3.8 51. y = 5x – 15 52. y = 4x + 6 1 20 53. y = – 2x + 7 54. y = – 10x + 15 55. y = x 3 3 2 56. y = x – 1 57. y = – 3.2x + 30.86 58. y = 0.9x + 4.63 7 11 2 2 (B) – 2x + 3y = 11 (C) y = x + 59. (A) m = 3 3 3 3 3 1 60. (A) m = (B) 3x – 2y = – 1 (C) y = x + 2 2 2 5 5 7 61. (A) m = (B) 5x + 4y = – 14 (C) y = – x 4 4 2 23 4 4 62. (A) m = (B) 4x + 5y = 23 (C) y = – x + 5 5 5 63. (A) Not defined (B) x = 5 (C) None 65. (A) m = 0 (B) y = 5 (C) y = 5 66. (A) Not defined (B) x = 2 (C) None 67. The graphs have the same y int., (0, 2). 68. The graphs have the same slope, – 0.5. 69. C = 124 + 0.12x; 1,050 donuts 70. C = 1,200 + 45x; 80 picnic tables 71. (A) C = 75x + 1,647 (B) (C) The y int., $1,647, C is the fixed cost 15,000 and the slope, 10,000 $75, is the cost 5,000 per club. A-3 (B) $662 billion S 600 300 0 10 20 t Years since 2000 Copyright © Pearson Education, Inc. Answers 16. (A) Operating Income (millions) A-4 2 13. (A) y = – x 3 (B) y = 3 (1.2) 14. (A) 3x + 2y = 1 (B) y = 5 (C) x = – 2 (1.2) 25 30 (1.1) 16. u = 36 (1.1) 17. x = (1.1) 18. x = 21 (1.1) 15. x = 2 11 19. x = 4 (1.1) 20. x 6 4 or 1 – ∞, 42 (1.1) (B) $37.2 billion I 12. Vert. line: x = – 6; hor. line: y = 5 (1.2) 40 20 0 17. (A) 10 20 t Years since 2000 (B) 2°F Ethylene Glycol (%wt) y (C) 22.75% 80 22. x 6 – Propylene Glycol (%wt) y 24. (B) 7°F (C) 25.9% (C) 60 (A) y 10 30 1. x = 2.8 (1.1) 2. x = 2 (1.1) 3. y = 1.8 – 0.4x (1.1) 4 7 13 13 or a – ∞ , b 4. x = y + (1.1) 5. y 6 3 3 4 4 (1.1) x (1.1) x (1.1) 7. x Ú 8. 9 9 or c , ∞ b 2 2 (1.2) y 5 x 10. x int. = 9; y int. = – 6; slope = (B) A vert. line 4 (C) The x axis (D) An oblique line with x int. 12 and y int. 3 2A – bh S – P 9 (1.2) 28. (1.1) 29. (1.1) 30. a 6 0 and b any real h St number (1.1) 31. Less than (1.1) 32. The graphs appear to be perpendicular to each other. (It can be shown that if the slopes of two slant lines are the negative reciprocals of each other, then the two lines are perpendicular.) (1.2) 33. $75,000 (1.1) 34. 9,375 DVDs (1.1) 35. (A) m = 132 – 0.6x (B) M = 187 – 0.85x (C) Between 120 and 170 beats per minute (D) Between 102 and 144.5 beats per minute (1.3) 36. (A) V = 224,000 – 15,500t (B) $38,000 (1.2) 37. (A) R = 1.6C (B) $192 (C) $110 (D) The slope is 1.6. This is the rate of change of retail price with respect to cost. (1.2) 38. $400; $800 (1.1) 39. Demand: p = 5.24 – 0.00125x; 1,560 bottles (1.2) 40. (A) T (B) – 30°F (C) 45% (1.3) 40 with x int. – 48 60 M 2 (1.2) 3 20 10 0 20 40 t Years since 1990 42. (A) The CPI is increasing at a rate of 4.295 units per year. (B) 276.62 (1.3) 43. (A) The rate of change of tree height with respect to Dbh is 0.74. (B) Tree height increases by about 0.74 ft. (C) 21 ft (D) 16 in. (1.3) 2 11. y = – x + 6 (1.2) 3 y 10 3 4 41. (A) The dropout rate is decreasing at a rate of 0.308 percentage points (C) 2026 (1.3) per year. (B) r 6. 1 … x 6 3 or [1, 3) 4 9. 2x + 3y = 12 (1.2) 5 27. (A) An oblique line through the origin with slope – Dropout Rate (%) y 9 2 x (1.1) 7 8 (1.2) 26. The graph of x = – 3 is a vert. line with x int. – 3, and the graph of y = 2 is a hor. (B) y line with y int. 2. (1.2) 0 12 40 80 120 Chapter 1 Review Exercises 3 (1.1) 5 x 19. (A) The rate of change of height with respect to Dbh is 1.37 ft/in. (B) Height increases by approximately 1.37 ft. (C) 18 ft (D) 20 in. 20. (A) The rate of change of height with respect to Dbh is 1.66 ft/in. (B) Height increases by approximately 1.66 ft. (C) 15 ft (D) 18 in. 21. (A) Undergraduate male enrollment is increasing at a rate of 87,000 students per year; undergraduate female enrollment is increasing at a rate of 140,000 students per year. (B) Male: 8.6 million; female: 11.5 million (C) 2026 22. (A) Graduate male enrollment is increasing at a rate of 11,000 students per year; graduate female enrollment is increasing at a rate of 31,000 students per year. (B) Male: 1.3 million; female: 2.1 million (C) 2037 23. y = 0.061x + 50.703; 54.67°F 24. y = 0.051x + 30.166; 33.48 in. 25. Men: y = – 0.070x + 49.058; women: y = – 0.085x + 54.858; yes 26. Men: y = – 0.247x + 119.097; Women: y = – 0.122x + 128.494; no 27. Supply: y = 0.2x + 0.87; demand: y = – 0.15x + 3.5; equilibrium price = $2.37 28. Supply: y = 1.53x + 2.85; demand: y = – 2.21x + 10.66; equilibrium price: $6.05 1 x 4 3 8 x (1.1) 143 17 10 x 60 30 0 30 x Degrees ( F) 13 4 2 1 3 7 3 7 … x … or c , d 8 8 8 8 25. 90 x 1 143 143 or a – ∞, b 17 17 23. 1 6 x … 4 or (1, 44 24 260 230 0 30 x Degrees (8F) 18. (A) x 4 21. x Ú 1 or [1, ∞) (1.1) 10 x Copyright © Pearson Education, Inc.