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 = P(a - bP) -h, P(0) = Po dt where a, b, h, and P are positive constants. Suppose a = 3, b = 1, and h = 9 4 Determine whether the population becomes extinct in finite time. 3 2 O The population does not become extinct in finite time. The population becomes extinct in finite time for all values of Po The population becomes extinct in finite time if Po> z • The population becomes extinct in finite time if P₁ = 3 t= The population becomes extinct in finite time if P Po If so, find that time. (If not, enter NONE.) X X I 3+ calcP Operati Functia Symbol Relation Sets
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 = P(a - bP) -h, P(0) = Po dt where a, b, h, and P are positive constants. Suppose a = 3, b = 1, and h = 9 4 Determine whether the population becomes extinct in finite time. 3 2 O The population does not become extinct in finite time. The population becomes extinct in finite time for all values of Po The population becomes extinct in finite time if Po> z • The population becomes extinct in finite time if P₁ = 3 t= The population becomes extinct in finite time if P Po If so, find that time. (If not, enter NONE.) X X I 3+ calcP Operati Functia Symbol Relation Sets
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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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
dt
= P(a - bP) -h, P(0) = Po
9
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.
O The population becomes extinct in finite time if P <
The population does not become extinct in finite time.
The population becomes extinct in finite time for all values of Po
O The population becomes extinct in finite time if Po >
The population becomes extinct in finite time if P =
If so, find that time. (If not, enter NONE.)
t =
X
+
I
응
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