MANAGING MEDICATION

Classwork

If your doctor gives you medication, it's important to take the prescribed dosage on a regular basis. When you're a little kid, your parent tells you when to take the medication, but once you're an adult, you will have to remember to take the pills on your own. Of course, that is exactly the time when you start forgetting everything!

But why is it such a big deal when you forget your pill for a day? Does it really matter? Well, that depends on the particular medication. We will use the techniques of recursive sequences to investigate how different medications can behave differently in your body.

OK, let's say you start a course of Zapicillin on Monday and you take a full dose (100 milligrams). On Tuesday, you forget. Now, it's not as if the medication will disappear immediately out of your body after just one day. Some portion of it will still be there. Just how much of a portion will remain? That's the factor that varies with different medications. Research studies of Zapicillin have determined that approximately 71% of the medication will still be in your system on Tuesday, even though you forgot your pill. If you forget Wednesday's pill, then you will have 71% of what was there on Tuesday. It just continues on that way: each day your medication level will be about 71% of the previous day's level.

1) Approximately how many days would it take for half of the original dose to disappear? (This length of time is referred to as the "half-life" of the medication.)

2) Of course, we hope that you won't forget to take your pill. What happens if 71% of Monday's level remains and you add in Tuesday's dose as well?

3) Continue the sequence and make a table to show what happens to the medication level in your body if you take it regularly every day for three weeks. Call me over if you need help using the graphing calculator to do the recursion.

4) As you can see, you eventually approach an equilibrium level of medication. The drug is most effective if you maintain that level (within a certain tolerance). Suppose after three weeks of being very responsible, you forget your pill one day. Does forgetting just once have a big impact? How long does it take you to get back close to where you were before?

5) Sometimes people will realize that they forgot yesterday's pill. Then, to compensate, they take two pills the next day, and return to regular dosage on the following day. Is this a good strategy when taking Zapicillin? Make a sequence to simulate the situation. (Again, you don't have to get back to the exact level you had before, just within the tolerance you set.)

6) Some medications have a longer half-life than Zapicillin, so they remain in your system for a longer period of time. Suppose your doctor prescribes for you to take 15 mg of Phizamine every day. Knowing how much you love mathematics, your doctor reports to you that Phizamine has a half-life of 8 days. Whipping out your graphing calculator, you ask her how much of the drug remains after just one day. She tells you, as your math teacher always does, that you already have enough information to figure that out. Please do so.

7) Conduct some of the same experiments as you did with Zapicillin. What difference does the longer half-life make? Is the effect more dramatic when you forget to take your pill?

8) Several months later, your doctor tells you to increase your dose of Phizamine to 20 mg per day. You just bought a whole big expensive bottle of tablets that are 15 mg! Rather than throwing them away, you decide that you can just take a total of four tablets over the course of three days and still get very close to the correct medication level. (For example, you would take two tablets on Monday, then one on Tuesday, one on Wednesday, and back to two on Thursday, etc.) Is this a good plan? Conduct an experiment to find out.

9) Next consider a drug with a very short half-life-- something less than a day. Run the same experiments.

10) See if you can find a general relationship between the half-life of a drug and how long it takes to get very close to the equilibrium level.

11) Look for an explicit formula to predict the value of the equilibrium level.

12) Next time you are prescribed medication, ask your doctor what the half-life is.