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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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