Explanation Given Information: The provided statement is “The terms begin at 12 , oscillate and approach 6 ”. Formula Used: The general form of difference equation is y n = a y n − 1 + b ( with initial value y 0 ) Where a , b and y 0 are constant numbers. When the graph is monotonic choose a > 0 and for oscillating a < 0 . Also, if the graph is unbounded choose | a | > 1 and if approaches a value then | a | < 1 . To find b , put b 1 − a equals to that value. Calculation: Consider the provided statement that is “The terms begin at 12 , oscillate and approach 6 ”. Since, the terms begin at 12 . Suppose the beginning value as y 0 . Thus, y 0 = 12 . Since the graph is oscillating and approaching 6 . Thus, a should be a < 0 and | a | < 1 . Now suppose a = − 0.5 as the graph is monotonically increasing and also | a | < 1 . As, the graph is oscillating and approaching 6 . Find b , so that b 1 − a equals to 6. Therefore, put a = − 0.5 in b 1 − a which equals 6. b 1 − a = 6 b 1 − ( − 0.5 ) = 6 b = 6 ( 1.5 ) = 9 Now, put the value of a = − 0.5 and b = 9 in the general form of difference equation y n = a y n − 1 + b . Therefore, y n = − 0.5 y n − 1 + 9 Where y 0 = 12 . Thus, to find the value of y 1 , y 2 , y 3 , y 4 and y 5 . Case 1. For y 1 , put n = 1 and y 0 = 12 in the equation y n = − 0.5 y n − 1 + 9 . y n = − 0.5 y n − 1 + 9 y 1 = − 0.5 y 0 + 9 = − 0.5 ( 12 ) + 9 = 3 Thus, the value of y 1 = 3 . Case 2. For y 2 , put n = 2 and y 1 = 3 in the equation y n = − 0.5 y n − 1 + 9 . y n = − 0.5 y n − 1 + 9 y 2 = − 0.5 y 1 + 9 = − 0.5 ( 3 ) + 9 = 7

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ISBN: 9780134464053

Author: HAIR

Publisher: YUZU

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Chapter 12.3, Problem 34E

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To calculate: The difference equation and confirm the answer by graphing the difference equation when the terms begin at 12, oscillate and approach 6.

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Chapter 12.3, Problem 33E

Chapter 12.3, Problem 35E

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Chapter 12 Solutions

EBK FINITE MATHEMATICS & ITS APPLICATIO

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The difference equation and confirm the answer by graphing the difference equation when the terms begin at 12 , oscillate and approach 6 .

Solution Summary: The author calculates the difference equation by graphing the terms beginning at 12, oscillating and approaching 6.

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To calculate: The difference equation and confirm the answer by graphing the difference equation when the terms begin at 12, oscillate and approach 6.

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Chapter 12 Solutions