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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
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).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 8 steps with 8 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,