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Medicine and You (Grades 6-9)
Concepts Overview
| Healthy Hearts | Comparing Calories
| Medicine and You
| Answers
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More Math Concepts
 Part
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 patient’s system on day
1?
2.
How much medicine is in the patient’s 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 patient’s 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
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| 2
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| 3
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| 4
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| 5
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| 6
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| 7
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| 8
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| 9
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| 10 |
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| 11 |
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| 12 |
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| 13 |
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| 14 |
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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 patient’s system just prior to his
taking the pill.
6.
How much medicine is in the patient’s system on day
1 just before the pill is taken?
7.
How much medicine is in the patient’s 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 patient’s 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.
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