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

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Chapter2: Second-order Linear Odes
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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?
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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