Exponential Modeling

1. Provide, in visual format, any data, tables, or charts you use during the creation of your presentation. Tables, charts, and items listed below should all be present in a powerpoint presentation you will make for the class. Tables and charts should be detailed and informative and not be ‘slapdash’ creations.

2. It is common to take a drug (such as aspirin or an antibiotic) repeatedly as fixed time intervals. Suppose that an antibiotic has a half-life of 8 hours and a 100-milligram dose is taken every 8 hours. Write an exponential function that represents the decay of the antibiotic from the moment of the first dose to just prior to the next does (i.e., 8 hours after the first does).

3. How much antibiotic is in the bloodstream just prior to this next dose?

4. How much antibiotic is in the bloodstream just after this next dose?

5. Following the procedure in items #2-#4, calculate the amounts of antibiotic in the bloodstream just prior to, and just after doses at 16 hours, 24 hours, and 32 hours. Place your results in a single table.

6. Make a graph of the amount of antibiotic in the bloodstream for the first 32 hours after the first dose of the drug. What do you predict will happen to the amount of drug if the doses every 8 hours continue for several days or weeks? Explain.

7. Antibiotic prescriptions are generally provided for a limited time. If one is limited to a dose every 8 hours for 7 total days, what is the amount of drug in the bloodstream just after taking the final dose?

8. Based on the amount of antibiotic in the bloodstream just after the final dose (based on item #7 above), and knowing the half-life of the medication, estimate when the antibiotic falls to below 10-milligrams in the bloodstream after the final dose.