Population growth of any species is frequently modeled by an ODE of the form dN = aN - b dt N? N(0) = No where N is the population, an represents the birthrate, and 2 bN represents the death rate due to all causes, such as disease, competition for food supplies, and so on. If N, = 100,000, a = 0,1, and b = 0.00008, calculate N(t) using fourth order Runge-Kutta method for t = 0.0 to 20.0 years with h = 4. %3D %3D USE RUNGE - KUTTA METHOD

Population growth of any species is frequently modeled by an ODE of the form dN = aN - b dt N? N(0) = No where N is the population, an represents the birthrate, and 2 bN represents the death rate due to all causes, such as disease, competition for food supplies, and so on. If N, = 100,000, a = 0,1, and b = 0.00008, calculate N(t) using fourth order Runge-Kutta method for t = 0.0 to 20.0 years with h = 4. %3D %3D USE RUNGE - KUTTA METHOD

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Description: Population growth of any species isfrequently modeled by an ODE of theformdN= aN – bN?dtN(0) = Nowhere N is the population, aNrepresents the birthrate, and2bN represents the death rate due toall causes, such as disease,competition for food supplies,

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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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Population growth of any species is
frequently modeled by an ODE of the
form
dN
= aN – bN?
dt
N(0) = No
where N is the population, aN
represents the birthrate, and
2
bN represents the death rate due to
all causes, such as disease,
competition for food supplies, and
so on. If N, = 100,000, a = 0,1, and b
= 0.00008, calculate N(t) using
fourth order Runge-Kutta method for
t = 0.0 to 20.0 years with h = 4.
%3D
USE RUNGE - KUTTA METHOD

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