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)²₂ λ = μ E (X₂) = x-μ Ot + i, λ= μ.
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)²₂ λ = μ E (X₂) = x-μ Ot + i, λ= μ.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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