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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.

Common Core Standards

Content Standards
Mathematical Practices