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Every year, 20% of the population of Mathtown moves to the suburbs and 30% of the population of the suburbs move to Mathtown. Let M₁ be the population of Mathtown in year k and let S be the population of the suburbs in year k. Then Let æk = Mk Sk sin (a) Then #k+1 = Ak where A = 8 ?х f Ω Mk+1 = 0.8Mk +0.35% Sk+1 = 0.2M +0.75k III ? P Suppose in 2020 the populations of Mathtown and its suburbs were 1,000,000 and 500,000, respectively. What are the populations in 2025? M2025 = Number Spoor Number

Every year, 20% of the population of Mathtown moves to the suburbs and 30% of the population of the suburbs move to Mathtown. Let M₁ be the population of Mathtown in year k and let S be the population of the suburbs in year k. Then Let æk = Mk Sk sin (a) Then #k+1 = Ak where A = 8 ?х f Ω Mk+1 = 0.8Mk +0.35% Sk+1 = 0.2M +0.75k III ? P Suppose in 2020 the populations of Mathtown and its suburbs were 1,000,000 and 500,000, respectively. What are the populations in 2025? M2025 = Number Spoor Number

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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Every year, 20% of the population of Mathtown moves to the suburbs and 30% of the population of the suburbs move to Mathtown. Let M₁ be the population of Mathtown in year k and let S be the population of the suburbs in year k. Then Let æk = Mk Sk sin (a) Then #k+1 = Ak where A = 8 ?х f Ω Mk+1 = 0.8Mk +0.35% Sk+1 = 0.2M +0.75k III ? P Suppose in 2020 the populations of Mathtown and its suburbs were 1,000,000 and 500,000, respectively. What are the populations in 2025? M2025 = Number $2025 = Number With this migration pattern, the populations stabilize over many years. Find this steady state. limk→00 Mk = Number limk→∞0 Sk = Number
Transcribed Image Text:Every year, 20% of the population of Mathtown moves to the suburbs and 30% of the population of the suburbs move to Mathtown. Let M₁ be the population of Mathtown in year k and let S be the population of the suburbs in year k. Then Let æk = Mk Sk sin (a) Then #k+1 = Ak where A = 8 ?х f Ω Mk+1 = 0.8Mk +0.35% Sk+1 = 0.2M +0.75k III ? P Suppose in 2020 the populations of Mathtown and its suburbs were 1,000,000 and 500,000, respectively. What are the populations in 2025? M2025 = Number $2025 = Number With this migration pattern, the populations stabilize over many years. Find this steady state. limk→00 Mk = Number limk→∞0 Sk = Number
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