Suppose that each year, 80% of residents living in state A stay in state A, while 20% of them move to state B. Also, 70% of the residents living in state B stay in state B, while 30% of them move to state A. Further, assume at t = 0 years, there are 2 million residents living in state A and 5 million residents living in state B, and let x, and yn represent the populations (in millions) of the states A and B, respectively, at time t = n years. Given that 2 (:) a Yn d 5 find the value of the number b.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Suppose that each year, 80% of residents living in state A stay in state A, while 20% of them
move to state B. Also, 70% of the residents living in state B stay in state B, while 30% of
them move to state A. Further, assume at t = 0 years, there are 2 million residents living in
state A and 5 million residents living in state B, and let xn and yYn represent the populations (in
millions) of the states A and B, respectively, at time t = n years. Given that
(:) - (: )()
Xn
a
b
Yn
d
5
find the value of the number h.
Transcribed Image Text:Suppose that each year, 80% of residents living in state A stay in state A, while 20% of them move to state B. Also, 70% of the residents living in state B stay in state B, while 30% of them move to state A. Further, assume at t = 0 years, there are 2 million residents living in state A and 5 million residents living in state B, and let xn and yYn represent the populations (in millions) of the states A and B, respectively, at time t = n years. Given that (:) - (: )() Xn a b Yn d 5 find the value of the number h.
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