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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 dP 3D Р(а — ЬР) — Һ, dt P(0) = Por where a, b, h, and P, are positive constants. Suppose a = 3, b = 1, and h = -. Determine whether the population becomes extinct in finite time. The population becomes extinct in finite time for all values of Po. 3 The population becomes extinct in finite time if P. 2 The population becomes extinct in finite time if Po 2 The population does not become extinct in finite time. 3 The population becomes extinct in finite time if P. If so, find that time. (If not, enter NONE.)

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 dP 3D Р(а — ЬР) — Һ, dt P(0) = Por where a, b, h, and P, are positive constants. Suppose a = 3, b = 1, and h = -. Determine whether the population becomes extinct in finite time. The population becomes extinct in finite time for all values of Po. 3 The population becomes extinct in finite time if P. 2 The population becomes extinct in finite time if Po 2 The population does not become extinct in finite time. 3 The population becomes extinct in finite time if P. If so, find that time. (If not, enter NONE.)

Linear Algebra: A Modern Introduction
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 dP 3D Р(а — ЬР) — Һ, dt P(0) = Por where a, b, h, and P, are positive constants. Suppose a = 3, b = 1, and h = -. Determine whether the population becomes extinct in finite time. The population becomes extinct in finite time for all values of Po. 3 The population becomes extinct in finite time if P. 2 The population becomes extinct in finite time if Po 2 The population does not become extinct in finite time. 3 The population becomes extinct in finite time if P. If so, find that time. (If not, enter NONE.)
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 dP 3D Р(а — ЬР) — Һ, dt P(0) = Por where a, b, h, and P, are positive constants. Suppose a = 3, b = 1, and h = -. Determine whether the population becomes extinct in finite time. The population becomes extinct in finite time for all values of Po. 3 The population becomes extinct in finite time if P. 2 The population becomes extinct in finite time if Po 2 The population does not become extinct in finite time. 3 The population becomes extinct in finite time if P. If so, find that time. (If not, enter NONE.)
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