generate new members at a rate of 2 member: h member is expected to stay a club member f the number of members of the club at any giv process. Given that the club started with 5 m of club members after the first two weeks? (Hi

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 30CM
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Question
A club recruit member either through active recruitment by its current members or
through advertising in neighborhood billboards. Suppose that each member of the
club recruit new members at a rate of 3 members per week and that advertising in
neighborhood billboards generate new members at a rate of 2 members per week.
Suppose further that each member is expected to stay a club member for 1 week,
on average. Assume that the number of members of the club at any given time
follows a birth and death process. Given that the club started with 5 members, what
is the expected number of club members after the first two weeks? (Hint: refer to
the theorem below)
Theorem
For a linear growth process with immigration and Xo = i, we have
0
· (e(x-μ)t - 1) + ie(x-μ)t, x‡μ
E (X₂) =
x-fl
Ot + i,
λ = μ.
Transcribed Image Text:A club recruit member either through active recruitment by its current members or through advertising in neighborhood billboards. Suppose that each member of the club recruit new members at a rate of 3 members per week and that advertising in neighborhood billboards generate new members at a rate of 2 members per week. Suppose further that each member is expected to stay a club member for 1 week, on average. Assume that the number of members of the club at any given time follows a birth and death process. Given that the club started with 5 members, what is the expected number of club members after the first two weeks? (Hint: refer to the theorem below) Theorem For a linear growth process with immigration and Xo = i, we have 0 · (e(x-μ)t - 1) + ie(x-μ)t, x‡μ E (X₂) = x-fl Ot + i, λ = μ.
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