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Q3. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population o P(t) of the fishery at a time t is given by dP E Р(а - bР) — Һ, P(0) = Po, %3D dt where a, b, h, and Po are positive constants. i) Solve this IVP. ii) Suppose a = 5, b = 1 and h = 4. Then Use part (i) to determine the long term behavior of the population for the cases 0 < Po < 1, 1 < Po < 4, and Po > 4. iii) Use the information in parts (i) and (ii) to determine whether the fishery population becomes extinct in finite time T. If so, find that time T.

Q3. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population o P(t) of the fishery at a time t is given by dP E Р(а - bР) — Һ, P(0) = Po, %3D dt where a, b, h, and Po are positive constants. i) Solve this IVP. ii) Suppose a = 5, b = 1 and h = 4. Then Use part (i) to determine the long term behavior of the population for the cases 0 < Po < 1, 1 < Po < 4, and Po > 4. iii) Use the information in parts (i) and (ii) to determine whether the fishery population becomes extinct in finite time T. If so, find that time T.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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please explain all steps, show detailed solutions and more explanation for part b. please do not take from others

 

Q3. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population o P(t) of the fishery at a time t is given by dP Р(а - bР) — Һ, dt P(0) = Po, where a, b, h, and Po are positive constants. i) Solve this IVP. = 4. Then Use part (i) to determine the long term behavior ii) Suppose a = of the population for the cases 0 < Po < 1, 1 < Po < 4, and Po > 4. iii) Use the information in parts (i) and (ii) to determine whether the fishery population becomes extinct in finite time T. If so, find that time T. 5, 6 = 1 and h
Transcribed Image Text:Q3. If a constant number h of fish are harvested from a fishery per unit time, then a model for the population o P(t) of the fishery at a time t is given by dP Р(а - bР) — Һ, dt P(0) = Po, where a, b, h, and Po are positive constants. i) Solve this IVP. = 4. Then Use part (i) to determine the long term behavior ii) Suppose a = of the population for the cases 0 < Po < 1, 1 < Po < 4, and Po > 4. iii) Use the information in parts (i) and (ii) to determine whether the fishery population becomes extinct in finite time T. If so, find that time T. 5, 6 = 1 and h
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