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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
