Chapter 9.2, Problem 46E

Analyzing models The following models were discussed in Section 9.1 and reappear in later sections of this chapter. In each case, carry out the indicated analysis using direction fields.

Drug infusion 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 = 10 mg/hr and k = 0.05 hr⁻¹.

1. a. Draw the direction field, for 0 ≤ t ≤ 100, 0 ≤ y ≤ 600.
2. b.  For what initial values m(0) = A are solutions increasing? Decreasing?
3. c. What is the equilibrium solution?