Acetaminophen is one of the most popular over-the-counter pain relievers in the country, but it’s also one of the most common causes of liver failure. There isn’t a big difference between helpful and harmful dosages, and sometimes even following manufacturer recommendations isn’t enough to keep people out of harm’s way.

In this lesson students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

Students will

Given acetaminophen’s half-life, calculate its hourly rate of elimination from the body

Write an exponential rule for determining how much of the drug remains in a person’s body after a given time

Use logarithms to determine the required time until a person’s body contains a given amount of the drug

Describe how the amount of medication changes over time during a period of continued use

Discuss some of the dangers of exceeding the recommended dosage guidelines

Discuss what drug manufacturers should do to help prevent accidental acetaminophen overdoses

Before you begin

Students should be familiar with writing rules describing exponential decay. They will need to use logarithms to solve for variable exponents, and they should be able to apply basic rules of exponents and logarithms, for instance that (a)^{bc} = (a^{b})^{c} and log(a^{b}) = b log(a).

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Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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Building Functions (BF), Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE)

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Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)

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Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)