MS-Sol-EE-C03

MS-Sol-EE-C03 - CHAPTER 3 EXPONENTIAL FUNCTIONS Section 3.1...

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CHAPTER 3 EXPONENTIAL FUNCTIONS EXERCISE 3.1 Section 3.1 Properties and graphs of exponential functions (page 59) 1. 27 4 3 4 3 = (3 3 ) = 3 4 = 81 2. 16 3 4 3 4 = (2 4 ) = 2 3 = 8 3. 4 1 = 2 1 = ) (2 1 = 8 2 3 2 3 3 2 - 4. 125 1 = 5 1 = ) (5 1 = 25 3 2 3 2 2 3 - 5. 7 1 = 7 1 = 49 1 2 1 2 2 1 6. 3 5 = 3 5 = 625 81 4 1 4 4 4 1 - 7. 3 2 3 3 2 ] ) 6 ( [ = ) 216 ( - - = 36 8. 5 2 1 2 5 ] ) 36 ( [ = ) 36 ( - - This is undefined. 9. ) 2 ( 2 = ) 2 ( 2 = ) 128 ( 2 4 3 7 4 7 3 7 4 3 - - - = 2 10. 9 1 = 3 1 = ] 3 [ = )] 3 ( 3 [ = )] 27 ( 3 [ 2 1 2 1 4 2 1 3 4 2 - - - - - 35
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C HAPTER 3 E XPONENTIAL F UNCTIONS 11. n n n 16 8 2 3 + × = n n n ) 2 ( ) 2 ( 2 4 3 3 + × = n n n 4 9 3 2 2 2 + × = 2 n + (3 n + 9) – 4 n = 2 9 12. 1 3 2 2 243 9 27 + - - × n n n = 1 5 3 2 2 2 3 ) 3 ( ) 3 ( ) 3 ( + - - × n n n = 5 5 6 4 6 3 3 3 3 + - - × n n n = 3 (3 n – 6) + (4 n – 6) – (5 n + 5) = 3 2 n – 17 13. 6 2 25 ) 5 ( n n - = 6 1 2 2 2 1 ] ) 5 [( ) 5 ( n n - = 3 1 2 5 5 n n - = 3 ) 1 2 ( 5 n n - - = 1 6 5 - n 14. 5 1 3 2 32 16 - + n n = 5 1 1 5 3 1 2 4 ] ) 2 [( ] ) 2 [( - + n n = 1 3 8 3 4 2 2 - + n n = ) 1 ( ) 3 8 3 4 ( 2 - - + n n = 3 11 3 2 + n 15. (a) x 1 1.4 1.41 1.414 1.414 2 6 x 6 12.286 0 12.508 2 12.598 1 12.602 6 (b) 6 2 = 12.60 (4 sig. fig.) 16. (a) x 3 3.14 3.141 5 3.141 592 3.141 592 65 1.3 x 2.197 2.279 20 2.280 10 2.280 15 2.280 15 (b) 1.3 π = 2.280 2 (5 sig. fig.) 36
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S ECTION 3.1 P ROPERTIES AND G RAPHS OF E XPONENTIAL F UNCTIONS 17. x - 1 0 1 2 3 y = 3 x 1 3 1 3 9 27 18. x - 1 0 0.5 1 1.5 y = 10 x 0.1 1 3.16 10 31.6 37
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C HAPTER 3 E XPONENTIAL F UNCTIONS 19. x - 2 - 1 0 1 y = x 4 1 16 4 1 1 4 20. x - 3 - 2 - 1 0 1 2 y = (0.6) x 4.63 2.78 1.67 1 0.6 0.36 38
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S ECTION 3.1 P ROPERTIES AND G RAPHS OF E XPONENTIAL F UNCTIONS 21. x - 2 - 1 0 1 2 y = 4 x + 4 - x 16 1 16 4 1 4 2 4 1 4 16 1 16 22. x - 2 - 1 0 1 2 y = 4 x - 4 - x - 15 15 16 - 3 3 4 0 3 3 4 15 15 16 39
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C HAPTER 3 E XPONENTIAL F UNCTIONS 23. 24. 25. Note: The graph of y = g ( x ) = x - 8 is the mirror image of the graph of y = f ( x ) = 8 x about the y -axis. 40
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S ECTION 3.1 P ROPERTIES AND G RAPHS OF E XPONENTIAL F UNCTIONS 26. Note: The graph of y = g ( x ) = 1 5 . 2 + x can be obtained by shifting the graph of y = f ( x ) = 2 5 . x one unit upward. 27. Note: The graph of y = g ( x ) = 6 2 x - can be obtained by shifting the graph of y = f ( x ) = 6 x two units to the right. 41
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HAPTER 3 E XPONENTIAL F UNCTIONS 28. Note: The graph of x x g y - = = 3 2 4 ) ( can be obtained by reflecting the graph of y = f ( x ) = x 3 2 about the x -axis (it is the graph of y = x - 3 2 ) and then shifting it 4 units upward. 29.
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This note was uploaded on 10/17/2011 for the course IELM 3010 taught by Professor Fugee during the Winter '11 term at HKUST.

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MS-Sol-EE-C03 - CHAPTER 3 EXPONENTIAL FUNCTIONS Section 3.1...

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