A medication is administered to a patient. The amount, in milligrams, of the medication in the patient at time t hours is modeled by a function y = A(t) that satisfies the differential equation dy 12- y 3 At time dt == 0 hours, there are 0 milligrams of the medication in the patient. =
A medication is administered to a patient. The amount, in milligrams, of the medication in the patient at time t hours is modeled by a function y = A(t) that satisfies the differential equation dy 12- y 3 At time dt == 0 hours, there are 0 milligrams of the medication in the patient. =
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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Transcribed Image Text:6. A medication is administered to a patient. The amount, in milligrams, of the medication in the patient at
dy 12- y
time t hours is modeled by a function y = A (t) that satisfies the differential equation
dt
3
t = 0 hours, there are 0 milligrams of the medication in the patient.
(a) A portion of the slope field for the differential equation
curve through the point (0, 0).
ga
y
1 1/
dy
dt
=
with initial condition A(0) = 0.
12- y
3
| | || | || | || | ||
=
is given below. Sketch the solution
(b) Using correct units, interpret the statement lim A(t) = 12 in the context of this problem.
tI8
At time
(c) Use separation of variables to find y = A (t), the particular solution to the differential equation
dy
12- y
dt
3
Transcribed Image Text:(d) A different procedure is used to administer the medication to a second patient. The amount, in milligrams,
of the medication in the second patient at time t hours is modeled by a function y = B(t) that satisfies the
At time t = 1 hour, there are 2.5 milligrams of the medication in
y
dy
differential equation = 3
dt
t+2
the second patient. Is the rate of change of the amount of medication in the second patient increasing or
decreasing at time t = 1? Give a reason for your answer.
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