4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution over time of the associated disease can be modeled as a dynamical system whose state vector at time t consists of the number of people who have not been exposed and are therefore susceptible, the number who are currently sick with the disease, and the number who have recovered and are now immune. Suppose that the associated 3 × 3 yearly transition matrix A has eigenvalues λ = 1,1,0, and that the eigenvectors corresponding to the first two eigenvalues are x1 = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The initial state vector for the population is given by = Vo = 500x₁+200x2 + 100x3 where the third eigenvector x3 is not given here. How many people will be sick with the disease 2 years later? (a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000
4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution over time of the associated disease can be modeled as a dynamical system whose state vector at time t consists of the number of people who have not been exposed and are therefore susceptible, the number who are currently sick with the disease, and the number who have recovered and are now immune. Suppose that the associated 3 × 3 yearly transition matrix A has eigenvalues λ = 1,1,0, and that the eigenvectors corresponding to the first two eigenvalues are x1 = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The initial state vector for the population is given by = Vo = 500x₁+200x2 + 100x3 where the third eigenvector x3 is not given here. How many people will be sick with the disease 2 years later? (a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000
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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The answer is c) but I don't know the process
Transcribed Image Text:4. After exposure to certain live pathogens, the body develops long-term immunity. The
evolution over time of the associated disease can be modeled as a dynamical system whose
state vector at time t consists of the number of people who have not been exposed and are
therefore susceptible, the number who are currently sick with the disease, and the number
who have recovered and are now immune. Suppose that the associated 3 × 3 yearly
transition matrix A has eigenvalues λ = 1, 2, 0, and that the eigenvectors corresponding to
>
the first two eigenvalues are x₁ = (60, 20, 30) and x₂ = (-60, -30, 90), respectively. The
initial state vector for the population is given by
Vo = 500x1 + 200x2 + 100x3
where the third eigenvector x3 is not given here. How many people will be sick with the
disease 2 years later?
(a) 15450 (b) 27000 (c) 8500 (d) 9700 (e) 4000
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