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The following difference equation describes a simple model of a certain economy, where Yk is the total income during year k, a is a than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consun the annual rate of private investment. Yk+2- a(1 + b)Yk+1 + abYk = 1 Find the general solution when a = 0.99 and b= 0.25. Find the general solution of the difference equation, rounding to two decimal places as needed. Choose the correct answer below. O A. Yk = 100(0.99)k + 100(0.25)* O B. Yk = c (0.99)* c2(0.25)* - 100 Oc. Yk = C1 (0.99k) + c2(0.25k) + 100 OD. YK = c1 (1.24)* -c2(0.25)* E. YK = (0.99)* + (0.25)* + 0.01 OF. Yk = c (1.24)* +c2(0.25)* + 1 O G. YK = C1 (1.24k) + c2(0.25k) +1 O H. Yk = c (0.99)* + c2(0.25)* + 100

The following difference equation describes a simple model of a certain economy, where Yk is the total income during year k, a is a than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consun the annual rate of private investment. Yk+2- a(1 + b)Yk+1 + abYk = 1 Find the general solution when a = 0.99 and b= 0.25. Find the general solution of the difference equation, rounding to two decimal places as needed. Choose the correct answer below. O A. Yk = 100(0.99)k + 100(0.25)* O B. Yk = c (0.99)* c2(0.25)* - 100 Oc. Yk = C1 (0.99k) + c2(0.25k) + 100 OD. YK = c1 (1.24)* -c2(0.25)* E. YK = (0.99)* + (0.25)* + 0.01 OF. Yk = c (1.24)* +c2(0.25)* + 1 O G. YK = C1 (1.24k) + c2(0.25k) +1 O H. Yk = c (0.99)* + c2(0.25)* + 100

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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The following difference equation describes a simple model of a certain economy, where Yk is the total income during year k, a is a constant less than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consumer spending affect the annual rate of private investment. YK+2- a(1+ b)YK+1 +abYk = 1 Find the general solution when a = 0.99 and b= 0.25. Find the general solution of the difference equation, rounding to two decimal places as needed. Choose the correct answer below. O A. YK = 100(0.99)k + 100(0.25)k O B. Yk =c1 (0.99)* .c2(0.25)* - 100 %3D Oc. Yk = C1 (0.99k) + c2(0.25k) + 100 O D. Yk =c1(1.24)*.cz(0.25)* O E. YK = (0.99)* + (0.25)* + 0.01 O F. YK =c4 (1.24)* +c2(0.25)* + 1 O G. Yk = C1 (1.24k) + c2(0.25k) + 1 O H. YK = c4 (0.99)* +c2 (0.25)* + 100
Transcribed Image Text:The following difference equation describes a simple model of a certain economy, where Yk is the total income during year k, a is a constant less than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consumer spending affect the annual rate of private investment. YK+2- a(1+ b)YK+1 +abYk = 1 Find the general solution when a = 0.99 and b= 0.25. Find the general solution of the difference equation, rounding to two decimal places as needed. Choose the correct answer below. O A. YK = 100(0.99)k + 100(0.25)k O B. Yk =c1 (0.99)* .c2(0.25)* - 100 %3D Oc. Yk = C1 (0.99k) + c2(0.25k) + 100 O D. Yk =c1(1.24)*.cz(0.25)* O E. YK = (0.99)* + (0.25)* + 0.01 O F. YK =c4 (1.24)* +c2(0.25)* + 1 O G. Yk = C1 (1.24k) + c2(0.25k) + 1 O H. YK = c4 (0.99)* +c2 (0.25)* + 100
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