Bloodstream Drug Concentrations

The following questions are about modelling drug concentrations in the blood over time. Questions A and B rely of the information in the table below:

 Measurement Time Drug 1 Concentration Drug 2 Concentration Initial Drug Administration 1.0 mg/ml 1.5 mg/ml 4 Hours after Administration 0.15 mg/m. 0.75 mg/ml

A. For this part assume that the function describing the concentration as as function of time is linear. Each data set in the above table represents a different drug and a different initial dose. For each set:

1) Sketch a graph of the concentration function, that is, graph the level of concentration vs. time . Assume concentrations are measured in milligrams per milliliter, and time is in hours.

2) Predict the time when the concentration will fall below 0.025 mg/ml

3) Predict the time when the blood will be free of the drug.

4) Predict what the graph of concentration level vs. time would look like if further doses of the drug were administrered every six hours for forty-eight hours.

5) Predict what the graph of concentration vs. time would look like if further doses of the drug were administrered every six hours indefinitely.

B. Now assume that the concentration of the drug in the blood decays exponentially. This model has been shown in clinical tests to be more realistic. For each set:

1) Sketch a graph of the concenration function, that is, graph the level of concentration vs. time. Assume concentrations are measured in milligrams per milliliters, and time is measured in hours.

2) Predict the time when the concentration fall below 0.025 mg/ml

3) Predict the time when the concentration in the blood will be free of the drug.

4) Predict what the graph of concentration level vs. time would look like if further doses of the drug were administrered every six hours for forty-eight hours.

5) predict what would happen to the concentration level of the drug if it were administered every six hours indefinitely.