In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: dR dt dW dt Answer= 0.07R(1-0.00025R) - 0.001 RW -0.04W+0.00004 RW Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer.
In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: dR dt dW dt Answer= 0.07R(1-0.00025R) - 0.001 RW -0.04W+0.00004 RW Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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![Given:
Step 2
de
dt
57
57
dR
dt
Equilibrium solutions
dw
dt
dw
dt
and
20
(ii) when
2 0.IR 1-0.0001 R ) - 0.003 RW
(R, W) =
= -0.01 W + 0.00004 RW
dk
d+
(i) when w=0
Hence,
0.00004 RW
0.01 W=0
W / 0.00004 R -0.01) =0
W =0
=>
-7
=>
30.
occur at the points.
(0,0) and (10,000, 0);
R = 250
=> R=0 d
0.00004 R = 0.01
R =
1000
។
0.1 R0.00001 RY -0.003 RW =0
0.1 R0.00001 RV =0
R (0.1-0.00001 R) =0
=7
(250, 32.5)
=> 0.1(250) - 0.00001(250) -0.003 (250) 0 =0
0.75 W = 24.375
W = 32.5
equilibrium
where
[de =0]
0.00001 R = 0.1
=> R = 10,000.
solutions
= 250.
are
(0,0), (10,000,0) and (250, 32.5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81d21141-6551-4f5f-aede-0a79467fdc0f%2F3596e5fd-fd6c-49c9-969f-223937a35202%2Fsseuvj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given:
Step 2
de
dt
57
57
dR
dt
Equilibrium solutions
dw
dt
dw
dt
and
20
(ii) when
2 0.IR 1-0.0001 R ) - 0.003 RW
(R, W) =
= -0.01 W + 0.00004 RW
dk
d+
(i) when w=0
Hence,
0.00004 RW
0.01 W=0
W / 0.00004 R -0.01) =0
W =0
=>
-7
=>
30.
occur at the points.
(0,0) and (10,000, 0);
R = 250
=> R=0 d
0.00004 R = 0.01
R =
1000
។
0.1 R0.00001 RY -0.003 RW =0
0.1 R0.00001 RV =0
R (0.1-0.00001 R) =0
=7
(250, 32.5)
=> 0.1(250) - 0.00001(250) -0.003 (250) 0 =0
0.75 W = 24.375
W = 32.5
equilibrium
where
[de =0]
0.00001 R = 0.1
=> R = 10,000.
solutions
= 250.
are
(0,0), (10,000,0) and (250, 32.5)
Transcribed Image Text:In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations
as follows:
dR
dt
dW
dt
Answer=
0.07R(1-0.00025R) - 0.001 RW
-0.04W+0.00004 RW
Find all of the equilibrium solutions.
Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For
example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves,
and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers
to the nearest integer.
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