Explanation Given Information: The provided statement is “The terms begin at 50 and monotonically decrease without bound”. 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 50 and monotonically decrease without bound”. Since, the terms begin at 50 . Suppose the beginning value as y 0 . Thus, y 0 = 50 . Since the graph is monotonically decreasing without bound. Thus, a should be a > 0 and | a | > 1 . Now suppose a = 2 as the graph is monotonically decreasing and also | a | > 1 . As, the graph is monotonically decreasing unbounded. Find b , so that b 1 − a equals to value. Since, the graph is decreasing unbounded. So, the possible value will be 51 of b which equals b 1 − a . Therefore, b 1 − a = 51 b 1 − 2 = 51 b = 51 ( − 1 ) = − 51 Now, put the value of a = 2 and b = − 51 in the general form of difference equation y n = a y n − 1 + b . Therefore, y n = 2 y n − 1 − 51 Where y 0 = 50 . 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 = 50 in the equation y n = 2 y n − 1 − 51 . y n = 2 y n − 1 − 51 y 1 = 2 y 0 − 51 = 2 ( 50 ) − 51 = 49 Thus, the value of y 1 = 49 . Case 2. For y 2 , put n = 2 and y 1 = 49 in the equation y n = 2 y n − 1 − 51 . y n = 2 y n − 1 − 51 y 2 = 2 y 1 − 51 = 2 ( 49 ) − 51 = 47 Thus, the value of y 2 = 47

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Author: HAIR

Publisher: YUZU

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Chapter 12.3, Problem 36E

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To calculate: The difference equation and confirm the answer by graphing the difference equation when the terms begin at 50 and monotonically decrease without bound.

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Chapter 12.3, Problem 35E

Chapter 12.4, Problem 1CYU

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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 50 and monotonically decrease without bound.

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To calculate: The difference equation and confirm the answer by graphing the difference equation when the terms begin at 50 and monotonically decrease without bound.

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Chapter 12 Solutions