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

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) (Show Source): You can put this solution on YOUR website!

So when ,

So,

.
.
.
So depending on the value of A the function is either increasing or decreasing.

.
Decreasing if
Increasing if
Constant if
.
.
.
As t gets large,

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