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) = Por 9 where a, b, h, and Po are positive constants. Suppose a = 3, b = 1, and h = 4 Determine whether the population becomes extinct in finite time. O The population becomes extinct in finite time if P > 3 2 O The population does not become extinct in finite time. The population becomes extinct in finite time if Po<. 3 2 O The population becomes extinct in finite time for all values of Po. 3 O The population becomes extinct in finite time if Po 2 If so, find that time. (If not, enter NONE.) 2P0 3(2-3P0) t = X
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) = Por 9 where a, b, h, and Po are positive constants. Suppose a = 3, b = 1, and h = 4 Determine whether the population becomes extinct in finite time. O The population becomes extinct in finite time if P > 3 2 O The population does not become extinct in finite time. The population becomes extinct in finite time if Po<. 3 2 O The population becomes extinct in finite time for all values of Po. 3 O The population becomes extinct in finite time if Po 2 If so, find that time. (If not, enter NONE.) 2P0 3(2-3P0) t = X
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
= P(a − bP) – h,
dt
P(0) = Por
9
where a, b, h, and Po are positive constants. Suppose a = 3, b = 1, and h =
4
Determine whether the population becomes extinct in finite time.
O The population becomes extinct in finite time if Po >
3
2
O The population does not become extinct in finite time.
● The population becomes extinct in finite time if P <
3
2
O The population becomes extinct in finite time for all values of Po.
3
2
O The population becomes extinct in finite time if Po
=
If so, find that time. (If not, enter NONE.)
2P0
3(2-3P0)
t =
X
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