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55. = 71-

55. = 71-

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Problems 73-86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. . (a) Graph f(x) = 3* and g(x) = 10 on the same Cartesian n Source: U.S. Census Bureau b) Shade the region bounded by the y-axis, f(x) = 3*, (3) Solve f(x) = g(x) and label the point of intersection b) Shade the region bounded by the y-axis, f(x) = 2*, 1L(2) Graph f(x) = 2 and g (x) = 12 on the same Cartesian and g(x) = 12 on the graph drawn in part (a). l) Solve f(x) = g(x) and label the point of intersection press irrational solutions in exact form. 46. 5* = 25 Problems 43) 47. 2' = 10 50. 2* = 1.5 48. 3 = 14 51. 5(2) = 8 54. 2r+1 = 5!-2r 52. 0.3 (40.2x) = 0.2 AS= 1.2 () 55. = 71-x 58. 0.31+x = 1.72r-1 = 5* 1A12 (0.5)-* 4l. 2 + 2-12 = 0 S 16 + 4** - 3 =0 3-4" + 4.2" + 8 = 0 56. 62. 32x + 3* - 2 = 0 66. 9* - 3*+1 + 1 = 0 59. 7-x = et 63. 32* + 3*+1 - 4 = 0 you 60. e*+3 = the 64. 22 + 2*+2 – 12 = 0 mal 70. 2.49* + 11 7* + 5 = 0 67. 25* - 8.5* = -16 68. 36* - 6.6* = -9 71. 4 - 10.4* = 3 72. 3 - 14.3* = 5 (e) sl v 76. e2r = x + 2 80. In (2x) = -x + 2 84. e - In x = 4 74. log2(x - 1) – log,(x + 2) = 2 77. e = x? 78. e = x 81. In x = x – 1 In.r= -r 82. In x = -x? 85. e* = In x a+ Inx = 4 86. e* = -In x Alications and Extensions 93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the same Solve f(x) = 3. What point is on the graph of f? (e Solve g(x) = 4. What point is on the graph of g? Solve f(x) = g(x). Do the graphs of f and g intersect? Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 2**1, and g(x) = 2x+2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). (c) If so, where? (d) Solve (f + g) (x) = 7. (e) Solve (f – 8) (x) = 2. & (x) = log3 (x + 5) and g (x) = log3 (x - 1). (2) Solve f(x) = 2. What point is on the graph of f? 6) Solve g (x) = 3. What point is on the graph of g? (6) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g) (x) = 3. (e) Solve (f – g) (x) = 2. 8. (a) If f(x) = 3**1 and g(x) = 2**2, graph f and g on the same Cartesian plane. (b) Find the point(s) of intersection of the g:ss of fand g by solving f(x) = g(x). Round areters to three decimal places. Label any intersection points on the graph drawn in part (a). (c) Based on the graph, solve f(x) > g(x}. * (0) If f(x) = 5*-1 and g(x) = 2*+1 graph f and g on the same Cartesian plane. O Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Label any intersection points on the graph drawn in part (a). O Based on the graph, solve f(x) > g(x). 3 dep 94. (a) Graph f(x) = 3*+1 and g(x) = 3*-2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) and g (x) = 3*-2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). 3*+1, a 95. (a) Graph f(x) = 2* – 4. (b) Find the zero of f. (c) Based on the graph, solve f(x) < 0. 96. (a) Graph g(x) = 3* – 9. (b) Find the zero of g. (c) Based on the graph, solve g(x) > 0. 97. A Population Model The resident population of the United States in 2018 was 327 million people and was growing at a rate of 0.7% per year. Assuming that this growth rate continues, the model P(t) = 327 (1.007) the population P (in millions of people) in year t. (a) According to this model, when will the population of the United States be 415 million people? 1-2018 represents a bat MI s intere (b) According to this model, when will the population of the United States be 470 million people? plane. 98. A Population Model The population of the world in 2018 was 7.63 billion people and was growing at a rate of 1.1% per year. Assuming that this growth rate continues, the model P(t) = 7.63(1.011)-2018 represents the population P (in billions of people) in year t. (a) According to this model, when will the population of the world be 9 billion people? (b) According to this model, when will the population of the world be 12.5 billion people? and g (x) = 10 on the graph drawn in part (a). on the graph drawn in part (a). plane. i the graph drawn in part (a). Source: U.S. Census Bureau
Transcribed Image Text:Problems 73-86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. . (a) Graph f(x) = 3* and g(x) = 10 on the same Cartesian n Source: U.S. Census Bureau b) Shade the region bounded by the y-axis, f(x) = 3*, (3) Solve f(x) = g(x) and label the point of intersection b) Shade the region bounded by the y-axis, f(x) = 2*, 1L(2) Graph f(x) = 2 and g (x) = 12 on the same Cartesian and g(x) = 12 on the graph drawn in part (a). l) Solve f(x) = g(x) and label the point of intersection press irrational solutions in exact form. 46. 5* = 25 Problems 43) 47. 2' = 10 50. 2* = 1.5 48. 3 = 14 51. 5(2) = 8 54. 2r+1 = 5!-2r 52. 0.3 (40.2x) = 0.2 AS= 1.2 () 55. = 71-x 58. 0.31+x = 1.72r-1 = 5* 1A12 (0.5)-* 4l. 2 + 2-12 = 0 S 16 + 4** - 3 =0 3-4" + 4.2" + 8 = 0 56. 62. 32x + 3* - 2 = 0 66. 9* - 3*+1 + 1 = 0 59. 7-x = et 63. 32* + 3*+1 - 4 = 0 you 60. e*+3 = the 64. 22 + 2*+2 – 12 = 0 mal 70. 2.49* + 11 7* + 5 = 0 67. 25* - 8.5* = -16 68. 36* - 6.6* = -9 71. 4 - 10.4* = 3 72. 3 - 14.3* = 5 (e) sl v 76. e2r = x + 2 80. In (2x) = -x + 2 84. e - In x = 4 74. log2(x - 1) – log,(x + 2) = 2 77. e = x? 78. e = x 81. In x = x – 1 In.r= -r 82. In x = -x? 85. e* = In x a+ Inx = 4 86. e* = -In x Alications and Extensions 93. (a) Graph f(x) = 2*+1 and g(x) = 2*+2 on the same Solve f(x) = 3. What point is on the graph of f? (e Solve g(x) = 4. What point is on the graph of g? Solve f(x) = g(x). Do the graphs of f and g intersect? Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) = 2**1, and g(x) = 2x+2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). (c) If so, where? (d) Solve (f + g) (x) = 7. (e) Solve (f – 8) (x) = 2. & (x) = log3 (x + 5) and g (x) = log3 (x - 1). (2) Solve f(x) = 2. What point is on the graph of f? 6) Solve g (x) = 3. What point is on the graph of g? (6) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where? (d) Solve (f + g) (x) = 3. (e) Solve (f – g) (x) = 2. 8. (a) If f(x) = 3**1 and g(x) = 2**2, graph f and g on the same Cartesian plane. (b) Find the point(s) of intersection of the g:ss of fand g by solving f(x) = g(x). Round areters to three decimal places. Label any intersection points on the graph drawn in part (a). (c) Based on the graph, solve f(x) > g(x}. * (0) If f(x) = 5*-1 and g(x) = 2*+1 graph f and g on the same Cartesian plane. O Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Label any intersection points on the graph drawn in part (a). O Based on the graph, solve f(x) > g(x). 3 dep 94. (a) Graph f(x) = 3*+1 and g(x) = 3*-2 on the same Cartesian plane. (b) Shade the region bounded by the y-axis, f(x) and g (x) = 3*-2 on the graph drawn in part (a). (c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a). 3*+1, a 95. (a) Graph f(x) = 2* – 4. (b) Find the zero of f. (c) Based on the graph, solve f(x) < 0. 96. (a) Graph g(x) = 3* – 9. (b) Find the zero of g. (c) Based on the graph, solve g(x) > 0. 97. A Population Model The resident population of the United States in 2018 was 327 million people and was growing at a rate of 0.7% per year. Assuming that this growth rate continues, the model P(t) = 327 (1.007) the population P (in millions of people) in year t. (a) According to this model, when will the population of the United States be 415 million people? 1-2018 represents a bat MI s intere (b) According to this model, when will the population of the United States be 470 million people? plane. 98. A Population Model The population of the world in 2018 was 7.63 billion people and was growing at a rate of 1.1% per year. Assuming that this growth rate continues, the model P(t) = 7.63(1.011)-2018 represents the population P (in billions of people) in year t. (a) According to this model, when will the population of the world be 9 billion people? (b) According to this model, when will the population of the world be 12.5 billion people? and g (x) = 10 on the graph drawn in part (a). on the graph drawn in part (a). plane. i the graph drawn in part (a). Source: U.S. Census Bureau
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