Pounding Headache
How much Tylenol can you safely take?
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 = (ab)c and log(ab) = b log(a).Common Core Standards
Content Standards
Mathematical Practices
Downloads
Shoutouts
Tylenol, This American Life
Related Lessons
Pyramid of Sleaza
How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.
Loan Ranger
How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.
I Remember
How much can you trust your memory? Students construct and compare linear and exponential models to explore how much a memory degrades each time it's remembered.
iPod dPreciation
How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.
Green Acres
How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.
Financial Aid
How much more do graduates earn, and is college worth the cost? Students use systems of linear equations to compare different educational options.
Prescripted
How should pharmaceutical companies decide what to develop? In this lesson, students use linear and quadratic functions to explore how much pharmaceutical companies expect to make from different drugs, and discuss ways to incentivize companies to develop medications that are more valuable to society.
Wage War
How much should companies pay their employees? Students graph and solve systems of linear equations in order to examine the effects of wage levels on labor and consumer markets, and they discuss the possible pros and cons of increasing the minimum wage.
House of Pain
Why are so many Americans dying from opiate overdoses? Students use exponential decay and rational functions to understand why addicted patients seek more and stronger opioids to alleviate their pain.
XBOX Xponential
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.
Pandemic
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.
Billions & Billions
How has the human population changed over time? Students develop exponential models to analyze human population growth and explore the impact this growth will have in areas around the world.
