a) Form the product PD and interpret its entries. b) Prediction of this population distribution after 10 years and after 15 years could be found from what matrix products?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
icon
Related questions
Question
Where row 1 shows how the metropolitan population M changed (80% remained in M
to S) and row 2 shows how the population of the surrounding çounties
changed. Currently, the population is evenly divided between the two areas, which can be
and 20% moved
represented by the row matrix.
P = [% in M % in S] = [50% 50%] = [0.5 0.5]
%3D
%3D
%3D
a) Form the product PD and interpret its entries.
b) Prediction of this population distribution after 10 years and after 15 years could be found
from what matrix products?
Transcribed Image Text:Where row 1 shows how the metropolitan population M changed (80% remained in M to S) and row 2 shows how the population of the surrounding çounties changed. Currently, the population is evenly divided between the two areas, which can be and 20% moved represented by the row matrix. P = [% in M % in S] = [50% 50%] = [0.5 0.5] %3D %3D %3D a) Form the product PD and interpret its entries. b) Prediction of this population distribution after 10 years and after 15 years could be found from what matrix products?
Suppose that for a certain metropolitan area and the surrounding counties during each 5
year period, an average of 20% of the metropolitan population M moves to the
surrounding counties and the rest remains. Similarly, suppose that in the same period,
an average of 30% of the surrounding counties' population S moves to the metropolitan
area and the rest remains. This population dynamic can be represented as the matrix
[80% 20%
[30% 70%
[0.8 0.21
L0.3 0.7]
D
%3D
Transcribed Image Text:Suppose that for a certain metropolitan area and the surrounding counties during each 5 year period, an average of 20% of the metropolitan population M moves to the surrounding counties and the rest remains. Similarly, suppose that in the same period, an average of 30% of the surrounding counties' population S moves to the metropolitan area and the rest remains. This population dynamic can be represented as the matrix [80% 20% [30% 70% [0.8 0.21 L0.3 0.7] D %3D
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Matrix Operations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning