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Consider a population that grows linearly following the recursive formula PN = PN-1 + 108, with initial population Po = 93. a) Find P₁ = , P₂ = ,P3 = N b) Give an explicit formula for PN = c) Find P100 =

Consider a population that grows linearly following the recursive formula PN = PN-1 + 108, with initial population Po = 93. a) Find P₁ = , P₂ = ,P3 = N b) Give an explicit formula for PN = c) Find P100 =

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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### Linear Population Growth Following a Recursive Formula Consider a population that grows linearly following the recursive formula \( P_N = P_{N-1} + 108 \), with an initial population \( P_0 = 93 \). a) Calculate the population for the first three periods: - \( P_1 = \_\_\_\_\_ \) - \( P_2 = \_\_\_\_\_ \) - \( P_3 = \_\_\_\_\_ \) b) Derive an explicit formula for \( P_N \): - \( P_N = \_\_\_\_\_ + \_\_\_\_\_ \times N \) c) Determine the population at the 100th period: - \( P_{100} = \_\_\_\_\_ \) ### Explanation of Graphs or Diagrams There are no graphs or diagrams provided in this content. The exercise involves calculating linearly growing population values using a given recursive formula and deriving an explicit expression for the population at any given period \(N\).
Transcribed Image Text:### Linear Population Growth Following a Recursive Formula Consider a population that grows linearly following the recursive formula \( P_N = P_{N-1} + 108 \), with an initial population \( P_0 = 93 \). a) Calculate the population for the first three periods: - \( P_1 = \_\_\_\_\_ \) - \( P_2 = \_\_\_\_\_ \) - \( P_3 = \_\_\_\_\_ \) b) Derive an explicit formula for \( P_N \): - \( P_N = \_\_\_\_\_ + \_\_\_\_\_ \times N \) c) Determine the population at the 100th period: - \( P_{100} = \_\_\_\_\_ \) ### Explanation of Graphs or Diagrams There are no graphs or diagrams provided in this content. The exercise involves calculating linearly growing population values using a given recursive formula and deriving an explicit expression for the population at any given period \(N\).
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