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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

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

Advanced Engineering Mathematics
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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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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