Continuation of Example 4, Section 1.2: Find the equilibrium value of the digoxin model. What is the significance of the equilibrium value?

Data from example 4

Digoxin is used in the treatment of heart disease. Doctors must prescribe an amount of medicine that keeps the concentration of digoxin in the bloodstream above an effective level without exceeding a safe level (there is variation among patients). For an initial dosage of 0.5 mg in the bloodstream, Table 1.2 shows the amount of digoxin a remaining in the bloodstream of a particular patient after n days, together with the change Δa_n each day.

Table 1.2

A scatterplot ofΔa_n versus a_n from Table 1.2 is shown in Figure 1.11. The graph shows that the change Δa_n during a time interval is approximately proportional to the amount of digoxin a_n present in the bloodstream at the beginning of the time interval. The slope of

Figure 1.11

the proportionality line through the origin is approximately k ≈–0.107/0.345≈– 0.310. Since the graph in Figure 1.11 shows the change Δa_n as a linear function of   a_n   with slope –0.31, we have Δa_n = –0.31a_n.