Consider the differential equation 96 p(p-1.75)(p-2.75) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below
Consider the differential equation 96 p(p-1.75)(p-2.75) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below
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
![dp
Consider the differential equation=p(p-1.75)(p-2.75) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below.
dt
(a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below.
OA.
AF
O B.
Ap
Q
G
(b) If the initial population is 3600 [that is, p(0) = 3.6], what can be said about the limiting population lim p(t)?
1→ +00
If p(0) = 3.6, then lim p(t)=. The population will
1+ +00
(c) If p(0) = 2, what can be said about the limiting population lim p(t)?
1→ +00
If p(0) = 2, then lim p(t)= The population will
1→ +00
(d) If p(0) = 0.4, what can be said about the limiting population lim p(t)?
14.0
If p(0) = 0.4, then lim p(t)=. The population will
1+00
(e) Can a population of 2400 ever increase to 2900?
Q
O C.
Ap
it ▼possible for a population of 2400 to increase to 2900. One solution of the given differential equation is the horizontal line p(t) = If the population were to increase from 2400 to 2900, the corresponding solution curve would
by the existence-uniqueness theorem.
Q
that horizontal line. This would
what is guaranteed](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87e9d353-9fbf-4544-8543-ad6243c7195a%2Fa90301a0-8da0-40db-933c-e3591fec39de%2Fdzqsxbi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:dp
Consider the differential equation=p(p-1.75)(p-2.75) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below.
dt
(a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below.
OA.
AF
O B.
Ap
Q
G
(b) If the initial population is 3600 [that is, p(0) = 3.6], what can be said about the limiting population lim p(t)?
1→ +00
If p(0) = 3.6, then lim p(t)=. The population will
1+ +00
(c) If p(0) = 2, what can be said about the limiting population lim p(t)?
1→ +00
If p(0) = 2, then lim p(t)= The population will
1→ +00
(d) If p(0) = 0.4, what can be said about the limiting population lim p(t)?
14.0
If p(0) = 0.4, then lim p(t)=. The population will
1+00
(e) Can a population of 2400 ever increase to 2900?
Q
O C.
Ap
it ▼possible for a population of 2400 to increase to 2900. One solution of the given differential equation is the horizontal line p(t) = If the population were to increase from 2400 to 2900, the corresponding solution curve would
by the existence-uniqueness theorem.
Q
that horizontal line. This would
what is guaranteed
Expert Solution
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 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
