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4. The evolution in time of a some specie population is modelled by the so-called logistic model = rP (1-P) dP dT where P is the size of the population (a non-dimensional quantity) in time 7,7 is the growth rate, and K is a constant called the carrying capacity. (We will briefly discuss in class this model in a future lecture.) Find the dimensions of r and K so that the model is dimensionally consistent. Then show that a non-dimensional form of the logistic model is dp dt 2 = p (1 - p).

4. The evolution in time of a some specie population is modelled by the so-called logistic model = rP (1-P) dP dT where P is the size of the population (a non-dimensional quantity) in time 7,7 is the growth rate, and K is a constant called the carrying capacity. (We will briefly discuss in class this model in a future lecture.) Find the dimensions of r and K so that the model is dimensionally consistent. Then show that a non-dimensional form of the logistic model is dp dt 2 = p (1 - p).

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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4. The evolution in time of a some specie population is modelled by the so-called logistic model P(1-B), dP dT = rP where P is the size of the population (a non-dimensional quantity) in time 7,r is the growth rate, and K is a constant called the carrying capacity. (We will briefly discuss in class this model in a future lecture.) Find the dimensions of r and K so that the model is dimensionally consistent. Then show that a non-dimensional form of the logistic model is dp dt = p (1 − p).
Transcribed Image Text:4. The evolution in time of a some specie population is modelled by the so-called logistic model P(1-B), dP dT = rP where P is the size of the population (a non-dimensional quantity) in time 7,r is the growth rate, and K is a constant called the carrying capacity. (We will briefly discuss in class this model in a future lecture.) Find the dimensions of r and K so that the model is dimensionally consistent. Then show that a non-dimensional form of the logistic model is dp dt = p (1 − p).
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