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A model for insect populations leads to the difference equations 1+a Nk where and a are positive constants. i) Write the equation in the form N+1 = Ng +R(N )N and hence identify the growth rate. %3D ii) Plot the graph of R(N) as a function of Ng. iii) Express the intrinsic growth rate r and the carrying capacity K, for this model, in terms of the parameters, a and 2. iv) Find the steady-state solution of this model and analyse the solution.

A model for insect populations leads to the difference equations 1+a Nk where and a are positive constants. i) Write the equation in the form N+1 = Ng +R(N )N and hence identify the growth rate. %3D ii) Plot the graph of R(N) as a function of Ng. iii) Express the intrinsic growth rate r and the carrying capacity K, for this model, in terms of the parameters, a and 2. iv) Find the steady-state solution of this model and analyse the solution.

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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In a species of animals a constant fraction of the population a = 5.3 are born each breeding season and a sonstant fraction B = 4.97 die. Formulate a difference equation for the population and find out the number of individuals after fifteen seasons given that the initial number is 987. Find the closed form solution of the fosulated difference equation. If the growth rate of the population is represented by r then interpret the solution obtained when i) r > 0 and ii) r< 0. 7 6. b) A model for insect populations leads to the difference equations k+1 1+a Nx where 2 and a are positive constants. i) Write the equation in the form N+ = Ng +R(N, )N and hence identify the growth rate. k+1 k ii) Plot the graph of R(N ) as a function of N. iii) Express the intrinsic growth rate r and the carrying capacity K, for this model, in terms of the parameters, a and 2. iv) Find the steady-state solution of this model and analyse the solution.
Transcribed Image Text:In a species of animals a constant fraction of the population a = 5.3 are born each breeding season and a sonstant fraction B = 4.97 die. Formulate a difference equation for the population and find out the number of individuals after fifteen seasons given that the initial number is 987. Find the closed form solution of the fosulated difference equation. If the growth rate of the population is represented by r then interpret the solution obtained when i) r > 0 and ii) r< 0. 7 6. b) A model for insect populations leads to the difference equations k+1 1+a Nx where 2 and a are positive constants. i) Write the equation in the form N+ = Ng +R(N, )N and hence identify the growth rate. k+1 k ii) Plot the graph of R(N ) as a function of N. iii) Express the intrinsic growth rate r and the carrying capacity K, for this model, in terms of the parameters, a and 2. iv) Find the steady-state solution of this model and analyse the solution.
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