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Mathline

Medicine and You (Grades 6-9)

Concepts Overview  |  Healthy Hearts |  Comparing Calories  |  Medicine and You  |  Answers  |  More Math Concepts

pillsPart of being healthy is dealing with being sick. At times, we need to take medicine to return to a healthier state. Scientists, doctors, and pharmacists use mathematics to determine how much medicine we need to take and how long the medicine stays in our bodies. Here are a number of problems that touch on this range of topics.

Each morning a patient must take a pill containing 50 mg of a certain medicine. Assume that the medicine is immediately introduced to his system. One of the things that our bodies do is wash stuff out of our systems. In the process of doing this, 40% of the medicine this patient takes is gone the next morning when it is time to take the next tablet.

1. How much medicine is in the patientís system on day 1?

2. How much medicine is in the patientís system on day 2 just before the pill is taken?

3. How much is in the patient's system on day 2 just after the pill is taken?

4. Fill in the dosage chart to show how much medicine is in the patientís system just after taking the pill each day.

Dosage Chart

Day Amount of Medicine in System Just Before Pill is Taken Amount of Medicine in System Just After Pill is Taken
1    
2    
3    
4    
5    
6    
7    
8    
9    
10    
11    
12    
13    
14    

5. If the patient were to continue taking one pill each morning, what is the maximum level of the medicine that would eventually accumulate in his body? Why?

Another way to look at this problem is to consider how much medicine is in the patientís system just prior to his taking the pill.

6. How much medicine is in the patientís system on day 1 just before the pill is taken?

7. How much medicine is in the patientís system on day 2 just before the pill is taken?

8. Fill in the rest of the table to show the minimal amount of medicine in the patientís system just before taking the pill each day. How does this relate to the amount of medicine in their system after taking the pill?

9. If the patient were to continue taking one pill each morning, what is the minimum level of medicine that would eventually accumulate in his body? Why?

One of the important issues in using medicine to get healthy is making sure that the medicine is maintained in the body at the proper level for the proper duration. For this medicine to work most effectively, it must maintain a level of at least 50 mg in the body over the course of 10 days.

10. If the patient always takes the medicine as prescribed, at what point will the level of medicine in his body not drop below 50 mg?

11. Suppose the patient skips day 7, and then continues taking the medicine on day 8. To what level will the medicine in the body drop just prior to taking the pill on day 8?

From this activity, you can probably see why the importance of continuing to take medicine as instructed even though you may start to feel better.