Why are so many Americans dying from opiate overdoses? Across the United States, families and communities have been devastated by opiate addiction. A patient breaks her arm and receives a powerful pain reliever such as Oxy-Contin, then ends up addicted to heroin or even fentanyl.

In this lesson, students use exponential decay and rational functions to understand why addicted patients seek more and stronger opioids to alleviate their pain. Students discuss the role that various parties played in creating the crisis and ways they can help to solve it.

Students will

Describe the deterioration of pain relief from a standard dosage of opioids using an exponential decay function.

Construct a rational function to model the increased dosage a patient would need to maintain complete pain relief

Discuss and debate the role that pharmaceutical companies, doctors, patients, and society at large can and should have in addressing the opioid epidemic in America.

Before you begin

Adjust timing as needed depending on students' familiarity with exponential decay. Students don't need to have mastered writing exponential decay functions -- they can reason intuitively about the functions they write -- but it will be helpful to have explored some functions that model decay previously.

How much should people pay for donuts? Students use linear, rational, and piecewise functions to describe the total and average costs of an order at Carpe Donut.

Topic:
Building Functions (BF), Interpreting Functions (IF)

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI), Similarity, Right Triangles, and Trigonometry (SRT)

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.

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

How do viruses spread through a population? Students use exponential growth and logarithms to model how a virus spreads through a population and evaluate how various factors influence the speed and scope of an outbreak.

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

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.

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

Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in Les Misérables, and explore the maximum height from which someone can safely jump.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF)

How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.

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

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.

How can we improve our calendar? Students examine some other ways to keep track of dates, and use number sense and function concepts to convert between different calendars.

Topic:
Building Functions (BF), Functions (F), Interpreting Functions (IF)

How much Tylenol can you safely take? 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.

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

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.

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

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

Topic:
Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)

How much should Nintendo charge for a video game console? Students use linear and quadratic models to analyze and discuss the relationship between the price of a Wii U console and profits for Nintendo.

Topic:
Creating Equations (CED), Building Functions (BF), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually pizza, and how much is crust.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

How do noise-canceling headphones work? In this lesson, students use transformations of trigonometric functions to explore how sound waves can interfere with one another, and how noise-canceling headphones use incoming sounds to figure out how to produce that sweet, sweet silence.

Topic:
Building Functions (BF), Interpreting Functions (IF)

How should pharmaceutical companies decide which drugs to develop? Students create linear and quadratic functions to explore how much pharmaceutical companies profit from different drugs and consider ways to incentivize companies to prioritize medications that are valuable to society.

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

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.

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

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

Topic:
Building Functions (BF), Creating Equations (CED)

How much should you bid in an auction? Students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.

Topic:
Building Functions (BF), Interpreting Functions (IF)

Is higher education a good investment? Students write and solve systems of linear equations to determine how long it would take to pay off various degrees and discuss the pros and cons of different educational paths.

Topic:
Building Functions (BF), Interpreting Functions (IF)

Should the government increase the minimum wage? Students use systems of linear equations to explore the relationship between wage and labor, analyze the economics of fast-food restaurants, and debate whether the federal government should increase the minimum wage.

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

How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.

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