Problem 10 (Sec 11.4) Consider the following model dP dt = r(M-P)P where M represents a carrying capacity. Suppose that a healthy population of some species is growing in a limited environment and that the current population Po is fairly close to the carrying capacity Mo. You might imagine a population of fish living in a freshwater lake in a wilderness area. Suddenly, a catastrophe such as the Mount St. Helens volcanic eruption contaminates the lake and destroys a significant part of the food and oxygen on which the fish depend. The result is a new environment with a carrying capacity M₁ considerably less than M。 and, in fact, less than the current population Po. Starting at some time before the catastrophe, sketch "before-and-after" curve that shows how the fish population responds to the change in the environment.
Problem 10 (Sec 11.4) Consider the following model dP dt = r(M-P)P where M represents a carrying capacity. Suppose that a healthy population of some species is growing in a limited environment and that the current population Po is fairly close to the carrying capacity Mo. You might imagine a population of fish living in a freshwater lake in a wilderness area. Suddenly, a catastrophe such as the Mount St. Helens volcanic eruption contaminates the lake and destroys a significant part of the food and oxygen on which the fish depend. The result is a new environment with a carrying capacity M₁ considerably less than M。 and, in fact, less than the current population Po. Starting at some time before the catastrophe, sketch "before-and-after" curve that shows how the fish population responds to the change in the environment.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 44EQ
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Transcribed Image Text:Problem 10 (Sec 11.4) Consider the following model
dP
dt
=
r(M-P)P
where M represents a carrying capacity. Suppose that a healthy population of
some species is growing in a limited environment and that the current population
Po is fairly close to the carrying capacity Mo. You might imagine a population
of fish living in a freshwater lake in a wilderness area. Suddenly, a catastrophe
such as the Mount St. Helens volcanic eruption contaminates the lake and
destroys a significant part of the food and oxygen on which the fish depend.
The result is a new environment with a carrying capacity M₁ considerably less
than M。 and, in fact, less than the current population Po. Starting at some
time before the catastrophe, sketch "before-and-after" curve that shows how
the fish population responds to the change in the environment.
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