150 125 100 75+ 50 1 25
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Suppose that a population develops according to the logistic equation
dP/dt= 0.06P − 0.0006P2
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.
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.)
P0
Which solutions are decreasing? (Enter your answer using interval notation.)
P0
(d) What are the equilibrium solutions? (Enter your answers as a comma-separated list.)
P =
Transcribed Image Text:The image represents a vector field plot on a graph with the horizontal and vertical axes ranging from 0 to 50 and 0 to 150, respectively.
### Description of the Vector Field:
- **Direction and Orientation**: The vectors are uniformly distributed across the graph, with a slight inclination pointing from the southwest to the northeast.
- **Magnitude**: The vectors maintain a consistent length throughout the field, indicating a uniform magnitude.
- **Density**: The density of the vectors remains the same across the graph, suggesting consistent spacing.
### Grid Lines:
- **Horizontal and Vertical Axes**: The axes are labeled at intervals of 10, with major grid lines corresponding to 0, 10, 20, 30, 40, and 50 on the x-axis, and 0, 25, 50, 75, 100, 125, and 150 on the y-axis.
- **Dashed Line**: A prominent horizontal dashed line is located at y = 100, possibly highlighting a specific value or threshold.
This vector field can be used educationally to illustrate concepts related to gradients, flow direction, or physical phenomena such as fluid dynamics or electromagnetic fields.
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