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 in the figure below. On the coordinate plane the horizontal axis is labeled t and the vertical axis is labeled P. There is a slope field in the first quadrant on the graph. The slopes are nearly horizontal at P = 0. As P increases, the slopes go up and right becoming more steep until about P = 50, then go up and right becoming less steep, become horizontal near P = 100, and go down and right becoming more steep until they exit the window near P = 150. Where are the slopes close to 0? (Enter your answers as a comma-separated list.) P = Where are the slopes 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 ∈
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 in the figure below. On the coordinate plane the horizontal axis is labeled t and the vertical axis is labeled P. There is a slope field in the first quadrant on the graph. The slopes are nearly horizontal at P = 0. As P increases, the slopes go up and right becoming more steep until about P = 50, then go up and right becoming less steep, become horizontal near P = 100, and go down and right becoming more steep until they exit the window near P = 150. Where are the slopes close to 0? (Enter your answers as a comma-separated list.) P = Where are the slopes 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 ∈
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
Related questions
Question
Suppose that a population develops according to the logistic equation
dP |
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 in the figure below.
On the coordinate plane the horizontal axis is labeled t and the vertical axis is labeled P. There is a slope field in the first quadrant on the graph. The slopes are nearly horizontal at P = 0. As P increases, the slopes go up and right becoming more steep until about P = 50, then go up and right becoming less steep, become horizontal near P = 100, and go down and right becoming more steep until they exit the window near P = 150.
Where are the slopes close to 0? (Enter your answers as a comma-separated list.)
P =
Where are the slopes 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 ∈
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill