2. The logistic equation for the population (in thousands) of a certain species is given by 2 = 3p? - 2p°. Complete parts (a) through (d) 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. OB. Ap Q Ap (b) If the initial population is 2700 (that is, p(0) = 2.7], what can be said about the limiting population lim p(t)? If p(0) = 2.7, then lim p(t) = 1.5 The population will decrease and level off. (c) If p(0) = 1.1, what can be said about the limiting population lim p(t)? t-+ 00 If p(0) = 1.1, then lim p(t) = The population wil (1)-
2. The logistic equation for the population (in thousands) of a certain species is given by 2 = 3p? - 2p°. Complete parts (a) through (d) 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. OB. Ap Q Ap (b) If the initial population is 2700 (that is, p(0) = 2.7], what can be said about the limiting population lim p(t)? If p(0) = 2.7, then lim p(t) = 1.5 The population will decrease and level off. (c) If p(0) = 1.1, what can be said about the limiting population lim p(t)? t-+ 00 If p(0) = 1.1, then lim p(t) = The population wil (1)-
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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Question
Transcribed Image Text:(d) Can a population of 2700 ever decline to 1100?
(2)
equation is the horizontal line p(t) =
it (3).
possible for a population of 2700 to decline to 1100. One solution of the given differential
If the population were to decline from 2700 to 1100, the corresponding solution curve
would (4).
that horizontal line. This would (5)
what is guaranteed by the existonce-uniqueness theorem.
(3) O is
is not
pass through
always be below
(1)
decrease without limit.
(2)
No,
(4)
(5) O contradict
decrease and level off.
O Yes,
O match
always be above
O increase without limit.
O increase and level off.
0000
![2.
The logistic equation for the population (in thousands) of a certain species is given by
2 = 3p? - 2p°. Complete parts (a) through (d) 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.
OB.
Ap
Q
(b) If the initial population is 2700 (that is, p(0) = 2.7], what can be said about the limiting population lim p(t)?
The population will decrease and level off.
If p(0) = 2.7, then lim p(t) =
1.5
(c) If p(0) = 1.1, what can be said about the limiting population lim p(t)?
t++ 00
If p(0) = 1.1, then lim p(t) =
The population will (1)-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F636cb0df-2252-4672-af55-9284a07ca8da%2F8f9a18e6-0161-4bb2-872c-84171ede583b%2F8uj1it_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
The logistic equation for the population (in thousands) of a certain species is given by
2 = 3p? - 2p°. Complete parts (a) through (d) 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.
OB.
Ap
Q
(b) If the initial population is 2700 (that is, p(0) = 2.7], what can be said about the limiting population lim p(t)?
The population will decrease and level off.
If p(0) = 2.7, then lim p(t) =
1.5
(c) If p(0) = 1.1, what can be said about the limiting population lim p(t)?
t++ 00
If p(0) = 1.1, then lim p(t) =
The population will (1)-
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