In tracking the propagation of a disease, a population can be divided into 3 groups: the portion that is susceptible, S(t), the portion that is infected, F(t), and the portion that is recovering, R(t). Each of these will change according to a differential equation: S' = F' = {{ R' so that the portion of the population that is infected is increasing in proportion to the number of susceptible people that contract the disease, and decreasing as a proportion of the infected people who recover. If we introduce the vector y [SF R], this can be written in matrix form as y' Ay. = If one of the solutions is y X1+300 e tla x2 + 400 e-t/c X3, where X1 [0 0 50,000], x₂ = [0 −1_1], and x3 = [b 32 −64]T, what are the values of a, b, and c? = || coito 5100 I
In tracking the propagation of a disease, a population can be divided into 3 groups: the portion that is susceptible, S(t), the portion that is infected, F(t), and the portion that is recovering, R(t). Each of these will change according to a differential equation: S' = F' = {{ R' so that the portion of the population that is infected is increasing in proportion to the number of susceptible people that contract the disease, and decreasing as a proportion of the infected people who recover. If we introduce the vector y [SF R], this can be written in matrix form as y' Ay. = If one of the solutions is y X1+300 e tla x2 + 400 e-t/c X3, where X1 [0 0 50,000], x₂ = [0 −1_1], and x3 = [b 32 −64]T, what are the values of a, b, and c? = || coito 5100 I
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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![In tracking the propagation of a disease, a population can be divided into 3 groups: the portion that is susceptible,
S(t), the portion that is infected, F(t), and the portion that is recovering, R(t). Each of these will change according
to a differential equation:
S'
F'
R' = E
so that the portion of the population that is infected is increasing in proportion to the number of susceptible people
that contract the disease, and decreasing as a proportion of the infected people who recover. If we introduce the
vector y = [S F R]T, this can be written in matrix form as y' = Ay.
If one of the solutions is
- tla
X1+300 e 1
y
+ 400 e-t/c x3,
X2
where x1
[00 50,000], x₂ = [0 -1 1], and x3
=
[b 32 −64]¹, what are the values of a, b, and c?
||
A co
52100
T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2Fbc0ed77d-6254-49d2-97a0-0a77d486ec8b%2Fxi1lqz_processed.png&w=3840&q=75)
Transcribed Image Text:In tracking the propagation of a disease, a population can be divided into 3 groups: the portion that is susceptible,
S(t), the portion that is infected, F(t), and the portion that is recovering, R(t). Each of these will change according
to a differential equation:
S'
F'
R' = E
so that the portion of the population that is infected is increasing in proportion to the number of susceptible people
that contract the disease, and decreasing as a proportion of the infected people who recover. If we introduce the
vector y = [S F R]T, this can be written in matrix form as y' = Ay.
If one of the solutions is
- tla
X1+300 e 1
y
+ 400 e-t/c x3,
X2
where x1
[00 50,000], x₂ = [0 -1 1], and x3
=
[b 32 −64]¹, what are the values of a, b, and c?
||
A co
52100
T
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