# Algebra

Concept Exercise 5

Problem: The level of a prescription drug in the human body over time can be found using the formula

L = D

1-( )

Where D is the amount taken every n hours and H is the drugs half-life in hours.

1) If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours then to what level does the drug build up over time?

2) If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?

3) What is the difference between taking 2.5 milligrams of Lorazepam every 12 hours and taking 5 milligrams every 24 hours?

Concept Exercise: Given the above problem, provide written responses to address the following points as precisely and thoroughly as possible.

1) Explain the problem in your own words.

2) What mathematical concepts learned in this module apply to this problem?

3) Explain the steps you must take to solve the problem.

4) What is the most difficult aspect of solving this problem?

5) Explain exactly what the answer means from a mathematical perspective.

[See the attached questions file.]

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#### Solution Preview

The solution file is attached.

Problem: The level of a prescription drug in the human body over time can be found using the formula

L = D

1-( )

Where D is the amount taken every n hours and H is the drugs half-life in hours.

1) If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours then to what level does the drug build up over time?

L = 2.5/[1 - (1/2)^(24/14)] = 3.596 mg

2) If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?

1 - (1/2)^(n/H) = D/L

(1/2)^(n/H) = 1 - (D/L)

(n/H) ln ...

#### Solution Summary

The level of a prescription drug in the human body over time is analyzed. Neat, step-by-step solutions are provided