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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Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.

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

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

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

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

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Topic:
Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)

How has the human population changed over time? Students build an exponential model for population growth and use it to make predictions about the future of our planet.

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

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Topic:
Building Functions (BF), Linear, Quadratic, and Exponential Models (LE)

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Topic:
Building Functions (BF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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

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