Suppose that a population develops according to the logistic equation dP = 0.05P – 0.0005P² dt where t is measured in weeks. (a) What is the carrying capacity? M = What is the value of k? k = (b) A direction field for this equation is shown. 150- 125 100 75 50 25 10 20 30 40 50 60 Where are the slopes close to 0? (Enter your answers as a comma-separated list.) P = Where are they largest? (Enter your answers as a comma-separated list.) P = Which solutions are increasing? (Enter your answer using interval notation.) Рое
Suppose that a population develops according to the logistic equation dP = 0.05P – 0.0005P² dt where t is measured in weeks. (a) What is the carrying capacity? M = What is the value of k? k = (b) A direction field for this equation is shown. 150- 125 100 75 50 25 10 20 30 40 50 60 Where are the slopes close to 0? (Enter your answers as a comma-separated list.) P = Where are they largest? (Enter your answers as a comma-separated list.) P = Which solutions are increasing? (Enter your answer using interval notation.) Рое
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:Suppose that a population develops according to the logistic equation
dP
= 0.05P – 0.0005P²
dt
where t is measured in weeks.
(a) What is the carrying capacity?
M =
What is the value of k?
k =
(b) A direction field for this equation is shown.
150-
125
100
75
50
25
10
20
30
40
50
60
Where are the slopes close to 0? (Enter your answers as a comma-separated list.)
P =
Where are they largest? (Enter your answers as a comma-separated list.)
P =
Which solutions are increasing? (Enter your answer using interval notation.)
Рое
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