5_3 - Chapter 5 Exponential and Logarithmic Functions 5.3...

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Chapter 5 659 Exponential and Logarithmic Functions 5.3 Exponential Functions 1. 64; 8 3 ( 29 2 = 2 2 = 4; 1 3 2 = 1 9 2. 3 x 2 + 5 x - 2 = 0 3 x - 1 ( 29 x + 2 ( 29 = 0 3 x - 1 = 0 x = 1 3 or x + 2 = 0 x = - 2 The solution set is - 2, 1 3 . 3. False 4. f x ( 29 - f c ( 29 x - c = 3 x - 5 - 3 c - 5 ( 29 x - c = 3 x - 5 - 3 c + 5 x - c = 3 x - 3 c x - c = 3 x - c ( 29 x - c = 3 5. True 6. 0,1 ( 29 , 1, a ( 29 , - 1, 1 a 7. 1 8. 4 9. False 10. False 11. (a) 3 2.2 11.212 (b) 3 2.23 11.587 (c) 3 2.236 11.664 (d) 3 5 11.665 12. (a) 5 1.7 15.426 (b) 5 1.73 16.189 (c) 5 1.732 16.241 (d) 5 3 16.242 13. (a) 2 3.14 8.815 (b) 2 3.141 8.821 (c) 2 3.1415 8.824 (d) 2 π 8.825
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Chapter 5 Exponential and Logarithmic Functions 660 14. (a) 2 2.7 6.498 (b) 2 2.71 6.543 (c) 2 2.718 6.580 (d) 2 e 6.581 15. (a) 3.1 2.7 21.217 (b) 3.14 2.71 22.217 (c) 3.141 2.718 22.440 (d) π e 22.459 16. (a) 2.7 3.1 21.738 (b) 2.71 3.14 22.884 (c) 2.718 3.141 23.119 (d) e π 23.141 17. e 1.2 3.320 18. e - 1.3 0.273 19. e - 0.85 0.427 20. e 2.1 8.166 21. x y = f x ( 29 f x + 1 ( 29 f x ( 29 –1 3 6 3 = 2 0 6 12 6 = 2 1 12 18 12 = 3 2 2 18 3 30 Not an exponential function since the ratio of consecutive terms is not constant. 22. x y = g x ( 29 g x + 1 ( 29 g x ( 29 –1 2 5 2 0 5 8 5 1 8 2 11 3 14 Not an exponential function since the ratio of consecutive terms is not constant.
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Section 5.3 Exponential Functions 661 23. x y = H x ( 29 H x + 1 ( 29 H x ( 29 –1 1 4 1 1/4 ( 29 = 4 0 1 4 1 = 4 1 4 16 4 = 4 2 16 64 16 = 4 3 64 Yes, an exponential function since the ratio of consecutive terms is constant with a = 4 . So the base is 4. 24. x y = F x ( 29 F x + 1 ( 29 F x ( 29 –1 2 3 1 2/3 ( 29 = 3 2 0 1 3/2 ( 29 1 = 3 2 1 3 2 9/4 ( 29 = 9 4 2 3 = 3 2 2 9 4 27/8 ( 29 = 27 8 4 9 = 3 2 3 27 8 Yes, an exponential function since the ratio of consecutive terms is constant with a = 3 2 . So the base is 3 2 .
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Chapter 5 Exponential and Logarithmic Functions 662 25. x y = f x ( 29 f x + 1 ( 29 f x ( 29 –1 3 2 3 3/2 ( 29 = 2 0 3 6 3 = 2 1 6 12 6 = 2 2 12 24 12 = 2 3 24 Yes, an exponential function since the ratio of consecutive terms is constant with a = 2 . So the base is 2. 26. x y = g x ( 29 g x + 1 ( 29 g x ( 29 –1 6 1 6 0 1 0 1 = 0 1 0 2 3 3 10 Not an exponential function since the ratio of consecutive terms is not constant. 27. x y = H x ( 29 H x + 1 ( 29 H x ( 29 –1 2 4 2 = 2 0 4 6 4 = 3 2 1 6 2 8 3 10 Not an exponential function since the ratio of consecutive terms is not constant.
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Section 5.3 Exponential Functions 663 28. x y = f x ( 29 f x + 1 ( 29 f x ( 29 –1 1 2 1/4 ( 29 1/2 ( 29 = 1 4 2 1 = 1 2 0 1 4 1/8 ( 29 ( 29 = 1 8 4 1 = 1 2 1 1 8 1/16 ( 29 1/8 ( 29 = 1 16 8 1 = 1 2 2 1 16 1/32 ( 29 1/16 ( 29 = 1 32 16 1 = 1 2 3 1 32 Yes, an exponential function since the ratio of consecutive terms is constant with a = 1 2 . So The base is 1 2 . 29. B 30. F 31. D 32. H 33. A 34. C 35. E 36. G 37. f ( x ) = 2 x + 1 Using the graph of y = 2 x , shift the graph up 1 unit. Domain: ( -∞ , ) Range: (1, ) Horizontal Asymptote: y = 1 38. f ( x ) = 2 x + 2 Using the graph of y = 2 x , shift the graph left 2 units. Domain: ( , ) Range: (0, ) Horizontal Asymptote: y = 0
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Chapter 5 Exponential and Logarithmic Functions 664 39. f ( x ) = 3 - x - 2 Using the graph of y = 3 x , reflect the graph about the y- axis, and shift down 2 units.
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This homework help was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

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5_3 - Chapter 5 Exponential and Logarithmic Functions 5.3...

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