Problem Description
Drug use
parameters
An initial dosage is taken. For each day thereafter, initial amount
a maintenance dose is taken. maintenance dose
The drug decays at a particular rate. decay rate
How much is in the bloodstream on any day?
Some examples
Digoxin is used in the treatment of heart disease.
Theopholine is used in the treatment of asthma.
Other situations
Change the time scale and model alcohol or sugar levels.
This solution was proposed by Lloyd McGuire of Southwestern University.
It has the advantage of showing how each dose decays and contributes to the amount in the bloodstream.
It has the disadvantage of being harder to extend and harder to mathematically analyze.
0.5 initial amount
0.1 maintenance dose
0.5 decay rate
day amt total
0 0.5 0.5
1 0.35 0.25 0.1
2 0.275 0.125 0.05 0.1
3 0.2375 0.0625 0.025 0.05 0.1
4 0.21875 0.03125 0.0125 0.025 0.05 0.1
5 0.209375 0.01563 0.00625 0.0125 0.025 0.05 0.1
6 0.2046875 0.00781 0.00313 0.00625 0.0125 0.025 0.05 0.1
7 0.20234375 0.00391 0.00156 0.00313 0.00625 0.0125 0.025 0.05 0.1
8 0.20117188 0.00195 0.00078 0.00156 0.00313 0.00625 0.0125 0.025 0.05 0.1
9 0.20058594 0.00098 0.00039 0.00078 0.00156 0.00313 0.00625 0.0125 0.025 0.05
10 0.20029297 0.00049 0.0002 0.00039 0.00078 0.00156 0.00313 0.00625 0.0125 0.025
11 0.20014648 0.00024 9.8E-05 0.0002 0.00039 0.00078 0.00156 0.00313 0.00625 0.0125
12 0.20007324 0.00012 4.9E-05 9.8E-05 0.0002 0.00039 0.00078 0.00156 0.00313 0.00625
13 0.20003662 6.1E-05 2.4E-05 4.9E-05 9.8E-05 0.0002 0.00039 0.00078 0.00156 0.00313
14 0.20001831 3.1E-05 1.2E-05 2.4E-05 4.9E-05 9.8E-05 0.0002 0.00039 0.00078 0.00156
15 0.20000916 1.5E-05 6.1E-06 1.2E-05 2.4E-05 4.9E-05 9.8E-05 0.0002 0.00039 0.00078
Drug Level in Bloodstream
0.6
0.5
0.4
drug amt
0.3
0.2
0.1
0
0 2 4 6 8 10 12 14 16
day
0.1
0.05 0.1
0.025 0.05 0.1
0.0125 0.025 0.05 0.1
0.00625 0.0125 0.025 0.05 0.1
0.00313 0.00625 0.0125 0.025 0.05 0.1
0.00156 0.00313 0.00625 0.0125 0.025 0.05 0.1
This solution was proposed by Adrianne Stropes and (independently) by Bryan Gibbs of Southwestern University.
It is also the one in "A first course in modeling" by Giordano, Weir, and Fox. The students had not seen the solution.
It has the advantage of being easily extendable.
See "soln 1" for a more intuitive approach.
0.5 initial amount
0.1 maintenance dose
0.5 decay rate
day amt total Drug Level in Bloodstream
0 0.5
1 0.35
0.6
2 0.275
3 0.2375
4 0.21875 0.5
5 0.209375
6 0.2046875 0.4
7 0.20234375
drug amt
8 0.20117188 0.3
9 0.20058594
10 0.20029297
11 0.20014648 0.2
12 0.20007324
13 0.20003662 0.1
14 0.20001831
15 0.20000916 0
0 5 10 15
day
en the solution.
Bloodstream
Series1
15 20