Determine whether the population becomes extinct in finite time. The population becomes extinct in finite time if Po > ● The population becomes extinct in finite time if Po< 0 3 The population becomes extinct in finite time if Po = 2 3 N/W The population becomes extinct in finite time for all values of Po O The population does not become extinct in finite time. If so, find that time. (If not, enter NONE.) t =

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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Investigate the following harvesting model both qualitatively and analytically.
If a constant number h of fish are harvested from a fishery per unit time, then a model for the population P(t) of the fishery
at time t is given by
where a,
dP
dt
=
t =
P(a - bP) - h, P(0) = Po,
b, h, and Po are positive constants. Suppose a 3, b = 1, and h
-
0
Determine whether the population becomes extinct in finite time.
3
2
The population becomes extinct in finite time if P
Po
The population becomes extinct in finite time if Po
=
If so, find that time. (If not, enter NONE.)
3
2
3
The population becomes extinct in finite time if P <
0
The population becomes extinct in finite time for all values of Po
The population does not become extinct in finite time.
9
nit
Transcribed Image Text:Investigate the following harvesting model both qualitatively and analytically. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population P(t) of the fishery at time t is given by where a, dP dt = t = P(a - bP) - h, P(0) = Po, b, h, and Po are positive constants. Suppose a 3, b = 1, and h - 0 Determine whether the population becomes extinct in finite time. 3 2 The population becomes extinct in finite time if P Po The population becomes extinct in finite time if Po = If so, find that time. (If not, enter NONE.) 3 2 3 The population becomes extinct in finite time if P < 0 The population becomes extinct in finite time for all values of Po The population does not become extinct in finite time. 9 nit
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