Suppose a certain population is initially absent from a certain area but begins migrating there at a rate of v individuals per day. Suppose further that this is an animal group that would normally grow at an exponential rate. Then the population after t days in the new area is given by N=L(e - 1), where ris a constant that depends on the species and the environment. If the new location proves unfavorable, then the value of r may be negative. In such a case, we can rewrite the population function as N = (a - 1), where a is less than 1. Under these conditions, what is the limiting value of the population? N =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
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Suppose a certain population is initially absent from a certain area but begins migrating there at a rate of v individuals per day. Suppose further that this is an animal group that would normally grow at an exponential rate. Then the
population after t days in the new area is given by
N = (e* - 1),
where r is a constant that depends on the species and the environment. If the new location proves unfavorable, then the value of r may be negative. In such a case, we can rewrite the population function as
N = (a* - 1),
where a is less than 1. Under these conditions, what is the limiting value of the population?
N =
Transcribed Image Text:Suppose a certain population is initially absent from a certain area but begins migrating there at a rate of v individuals per day. Suppose further that this is an animal group that would normally grow at an exponential rate. Then the population after t days in the new area is given by N = (e* - 1), where r is a constant that depends on the species and the environment. If the new location proves unfavorable, then the value of r may be negative. In such a case, we can rewrite the population function as N = (a* - 1), where a is less than 1. Under these conditions, what is the limiting value of the population? N =
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