63 monitoring progress and modeling with mathematics

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Introduction to Probability and Statistics
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Chapter 7 / Exercise 21
Introduction to Probability and Statistics
Beaver/Mendenhall
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6.3 Monitoring Progress and Modeling with Mathematics (pp. 314–316) 5. 3 2 = 9 7. 6 0 = 1 9. ( 1 2 ) 4 = 16 11. log 6 36 = 2 13. log 16 1 16 = 1 15. log 125 25 = 2 3 17. 4 19. 1 21. 4 23. 1 25. log 7 8, log 5 23, log 6 38, log 2 10 27. 0.778 29. 1.099 31. 2.079 33. 4603 m 35. x 37. 4 39. 2 x 41. 3 and 1 64 are in the wrong position; log 4 1 64 = 3 43. y = log 0.3 x 45. y = 2 x 47. y = e x + 1 49. y = 1 3 ln x 51. y = log 5 ( x + 9) 53. a. about 283 mi/h b. d = 10 ( s 65)/93 ; The inverse gives the distance a tornado will travel given the wind speed, s .
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Introduction to Probability and Statistics
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Chapter 7 / Exercise 21
Introduction to Probability and Statistics
Beaver/Mendenhall
Expert Verified
13. The graph of g is a translation 6 units up of the graph of f. y 4 2 2 4 4 6 x 10 g f 15. The graph of g is a translation 3 units right and 12 units up of the graph of f. y 4 2 x 4 2 20 40 60 80 Positive values of a vertically stretch ( a > 1) or shrink ( a < 1) the graph of f , h translates the graph of f left ( h < 0) or right ( h > 0), and k translates the graph of f up ( k > 0) or down ( k < 0). When a is negative, the graph of f is reflected in the x -axis. 20 17. The graph of g is a horizontal shrink by a factor of 1 2 of the graph of f. C; The graph of f is a translation 2 units left and 2 units down of the graph of the parent function y = 2 x 5. A; The graph of h is a translation 2 units right and 2 units down of the graph of the parent function y = 2 x 7. The graph of g is a translation 5 units up of the graph of y g f 4 6 2 4 4 2 6 x 4 6 2 g f 21. The graph of g is a horizontal shrink by a factor of 1 6 followed by a vertical stretch by a factor of 3 of the graph of f 4 2 2 4 4 6 8 The graph of g is a translation 1 unit down of the graph of y 4 2 2 4 4 2 6 8 x g f 11. The graph of g is a translation 7 units right of the graph of y 8 12 4 2 4 6 8 x 4 g f . x y g f b. 15 species c. about 3918 m 2 d. The number of species of fish increases; Sample answer: This makes sense because in a smaller pool or lake, one species could dominate another more easily and feed on the weaker species until it became extinct. 71. a. 2 3 b. 5 3 c. 4 3 d. 7 2 6.3 Maintaining Mathematical Proficiency (p. 316) 73. g ( x ) = 3 1 2 x 75. g ( x ) = 3 x + 2 77. quadratic; The graph is a translation 2 units left and 1 unit down of the parent quadratic function. 6.4 Vocabulary and Core Concept Check (p. 322) 1. Positive values of a vertically stretch ( a > 1) or shrink ( a < 1) the graph of f , h translates the graph of f left ( h < 0) or right ( h > 0), and k translates the graph of f up ( k > 0) or down ( k < 0). When a is negative, the graph of f is reflected in the x -axis. 6.4 Monitoring Progress and Modeling with Mathematics (pp. 322–324) 3. C; The graph of f is a translation 2 units left and 2 units down of the graph of the parent function y = 2 x 5. A; The graph of h is a translation 2 units right and 2 units down of the graph of the parent function y = 2 x 7. The graph of g is a translation 5 units up of the graph of y . . f. 9. The graph of g is a translation 1 unit down of the graph of y 4 2 2 4 4 2 6 8 x g f 11. The graph of g is a translation 7 units right of the graph of y 8 12 4 2 4 6 8 x 4 g f f. f.
A36 Selected Answers 47. The graph of g is a translation 6 units left of the graph of f ; x = 6 49. The graph of S is a vertical shrink by a factor of 0.118 followed by a translation 0.159 unit up of the graph of f ; For fine sand, the slope of the beach is about 0.05. For medium sand, the slope of the beach is about 0.09. For coarse sand, the slope of the beach is about 0.12. For very coarse sand, the slope of the beach is about 0.16.

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