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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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