The logistic equation for the population (in thousands) of a certain species is given by = 3p²-2p³. Complete parts (a) through (d) below. dp dt (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. O A. O B. Q (b) If the initial population is 3000 [that is, p(0) = 3], what can be said about the limiting population lim p(t)? If p(0) = 3, then lim p(t)=. The population will (c) If p(0)=1.2, what can be said about the limiting population lim p(t)? If p(0)=1.2, then lim p(t)=. The population will (d) Can a population of 1200 ever increase to 3000? possible for a population of 1200 to increase to 3000. One solution of the given 3000. One solution of the given what is guaranteed by the existence-uniqueness theorem. horizontal line. This would I I Q Q ✔ O C. Q differential equation is the horizontal line p(t) = differential equation is the horizontal line p(t)=. If the population were to increase from 1200 to 3000, the corresponding solution curve would that
The logistic equation for the population (in thousands) of a certain species is given by = 3p²-2p³. Complete parts (a) through (d) below. dp dt (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. O A. O B. Q (b) If the initial population is 3000 [that is, p(0) = 3], what can be said about the limiting population lim p(t)? If p(0) = 3, then lim p(t)=. The population will (c) If p(0)=1.2, what can be said about the limiting population lim p(t)? If p(0)=1.2, then lim p(t)=. The population will (d) Can a population of 1200 ever increase to 3000? possible for a population of 1200 to increase to 3000. One solution of the given 3000. One solution of the given what is guaranteed by the existence-uniqueness theorem. horizontal line. This would I I Q Q ✔ O C. Q differential equation is the horizontal line p(t) = differential equation is the horizontal line p(t)=. If the population were to increase from 1200 to 3000, the corresponding solution curve would that
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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![dp
The logistic equation for the population (in thousands) of a certain species is given by
= 3p²-2p³. Complete parts (a) through (d) below.
(a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below.
O A.
Ap
Q
Q
If p(0) = 3, then lim p(t)=. The population will
t→ +∞o
(c) If p(0)=1.2, what can be said about the limiting population lim p(t)?
If p(0)=1.2, then lim p(t)=. The population will
t→ +∞o
O B.
(b) If the initial population is 3000 [that is, p(0)=3], what can be said about the limiting population lim p(t)?
1 → +∞
(d) Can a population of 1200 ever increase to 3000?
it
horizontal line. This would
Ap
| |
*******
Q
C
Q
possible for a population of 1200 to increase to 3000. One solution of the given differential equation is the horizontal line p(t) =
▼what is guaranteed by the existence-uniqueness theorem.
O C.
Q
Q
If the population were to increase from 1200 to 3000, the corresponding solution curve would
that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf84dde2-f77b-4203-b744-f3414691451c%2Fad39cc9c-06ea-414b-9b94-3d3e28087a95%2Fdutduek_processed.png&w=3840&q=75)
Transcribed Image Text:dp
The logistic equation for the population (in thousands) of a certain species is given by
= 3p²-2p³. Complete parts (a) through (d) below.
(a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below.
O A.
Ap
Q
Q
If p(0) = 3, then lim p(t)=. The population will
t→ +∞o
(c) If p(0)=1.2, what can be said about the limiting population lim p(t)?
If p(0)=1.2, then lim p(t)=. The population will
t→ +∞o
O B.
(b) If the initial population is 3000 [that is, p(0)=3], what can be said about the limiting population lim p(t)?
1 → +∞
(d) Can a population of 1200 ever increase to 3000?
it
horizontal line. This would
Ap
| |
*******
Q
C
Q
possible for a population of 1200 to increase to 3000. One solution of the given differential equation is the horizontal line p(t) =
▼what is guaranteed by the existence-uniqueness theorem.
O C.
Q
Q
If the population were to increase from 1200 to 3000, the corresponding solution curve would
that
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