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# House of Pain

## Why are so many Americans dying from opiate overdoses?

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.

### REAL WORLD TAKEAWAYS

• Addiction to opioids is a public health crisis in the United States.
• Often, patients are prescribed opioids for legitimate pain concerns; over time, many patients experience less relief from the same dosage and so may take more and more to feel okay.
• Overdoses of these drugs is the leading cause of death in Americans under 50.
• Drug companies, doctors, and patients all played a role in created this crisis, and all could play a role in resolving the current opioid crisis in the United States.

### MATH OBJECTIVES

• 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.

Appropriate most times as students are developing conceptual understanding.
Algebra 2
Rational Functions
Algebra 2
Rational Functions
Content Standards F.BF.1 Write a function that describes a relationship between two quantities. (a) Determine an explicit expression, a recursive process, or steps for calculation from a context. (b) Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (c) (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. (a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (c) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Mathematical Practices MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.