2. First-Order Differential Equations: Suppose that the cumulative mumber of cases reported during an influenza outbreak in the Metro Detroit area is modeled with the logistic equation: dt 1000 z(0) -50 where r(t) is the total number of reported cases on day t. (a) Sketch the slope field of (1) over the range 0
2. First-Order Differential Equations: Suppose that the cumulative mumber of cases reported during an influenza outbreak in the Metro Detroit area is modeled with the logistic equation: dt 1000 z(0) -50 where r(t) is the total number of reported cases on day t. (a) Sketch the slope field of (1) over the range 0
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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![2. First-Order Differential Equations:
Suppose that the cumulative mumbCT of cases reported curing an influenza outbreak in
the Metro Detroit area is modeled with the logistic equation
dz
dt
=(1 – TO0)
1000
z(0)
-50
where r(t) is the total number of reported cases on day t.
(a) Sketch the slope field of (1) over the range 0<t< 100, 0<IS 1000. (Hint: Pick
regular intervals, like t =0, t = 25, r = 0, z =
250, etc.]
%3D
!!
1000
(b) Show that r(t)
is a solution to the initial value problem
1+ 19e-t
to c)=y+BAo qeretmpie
(c) What is the long-term behavior of (1)? In other words, according to the mc
how many people do we expect to contract influenza during the outbreak?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f812180-9157-4f42-a550-0a57853d73e0%2F81ace1e3-9248-4e7c-97b1-7745dae6ee9a%2Fpvibfxl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. First-Order Differential Equations:
Suppose that the cumulative mumbCT of cases reported curing an influenza outbreak in
the Metro Detroit area is modeled with the logistic equation
dz
dt
=(1 – TO0)
1000
z(0)
-50
where r(t) is the total number of reported cases on day t.
(a) Sketch the slope field of (1) over the range 0<t< 100, 0<IS 1000. (Hint: Pick
regular intervals, like t =0, t = 25, r = 0, z =
250, etc.]
%3D
!!
1000
(b) Show that r(t)
is a solution to the initial value problem
1+ 19e-t
to c)=y+BAo qeretmpie
(c) What is the long-term behavior of (1)? In other words, according to the mc
how many people do we expect to contract influenza during the outbreak?
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