SOLUTION: The delivery of a drug (such as an antibiotic) through an intravenous line may be modeled by the differential equation m'(t) + km(t) = I, where m(t) is the mass of the drug in the

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Question 1070768: The delivery of a drug (such as an antibiotic) through an intravenous line may be modeled by the differential equation m'(t) + km(t) = I, where m(t) is the mass of the drug in the blood at time t ≥0, k is a constant that describes the rate at which the drug is absorbed, and I is the infusion rate. Let I =15 mg/hr and k = 0.5 hr-1 . For what initial values m(0) = A are solutions increasing? decreasing? What is the equilibrium solution?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
dm%2Fdt%2B0.5m=15
m=Ce%5E%28-0.5t%29%2B15%2F0.5
m=Ce%5E%28-0.5t%29%2B30
So when t=0,
C%2B30=A
C=A-30
So,
m%28t%29=%28A-30%29e%5E%28-0.5t%29%2B30
.
.
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So depending on the value of A the function is either increasing or decreasing.
.
Decreasing if A%3E30
Increasing if A%3C30
Constant if A=30
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.
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As t gets large, m%28t%29=30