Suppose that a healthy population of some species is growing in a limited environment and that the current population P0 is fairly close to the carrying capacity M0. 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 M0 and, in fact, less than the current population P0. Starting at some time before the catastrophe, sketch a “before-and-after” curve that shows how the fish population responds to the change in environment.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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Suppose that a healthy
population of some species is growing in a limited environment
and that the current population P0 is fairly close to the carrying
capacity M0. 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 M0 and, in fact, less than
the current population P0. Starting at some time before the catastrophe,
sketch a “before-and-after” curve that shows how the fish
population responds to the change in environment.

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