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The logistic model of population growth uses the initial value problem: dN =r N dt N(1 - ) N(0) = No K where N(t) is the population at time t, K is the carrying capacity, and r is the growth rate. a) Determine the dimensions of the constant r, and show that by introducing appropriate dimen- sionless variables Ñ and i we can rewrite this equation in the form N = N(1 – Ñ). b) Find the general solution to the non-dimensionalized equation. dt

The logistic model of population growth uses the initial value problem: dN =r N dt N(1 - ) N(0) = No K where N(t) is the population at time t, K is the carrying capacity, and r is the growth rate. a) Determine the dimensions of the constant r, and show that by introducing appropriate dimen- sionless variables Ñ and i we can rewrite this equation in the form N = N(1 – Ñ). b) Find the general solution to the non-dimensionalized equation. dt

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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The logistic model of population growth uses the initial value problem: N(1-) . N(0) = No dN dt K where N(t) is the population at time t, K is the carrying capacity, and r is the growth rate. a) Determine the dimensions of the constant r, and show that by introducing appropriate dimen- sionless variables N and i we can rewrite this equation in the form dN b) Find the general solution to the non-dimensionalized equation. = Ñ(1 – Ñ).
Transcribed Image Text:The logistic model of population growth uses the initial value problem: N(1-) . N(0) = No dN dt K where N(t) is the population at time t, K is the carrying capacity, and r is the growth rate. a) Determine the dimensions of the constant r, and show that by introducing appropriate dimen- sionless variables N and i we can rewrite this equation in the form dN b) Find the general solution to the non-dimensionalized equation. = Ñ(1 – Ñ).
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