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Why are so many Americans dying from opiate overdoses? Students use exponential decay functions to understand how the effectiveness of a single dose of a prescription drug deteriorates over time. Then they'll construct a rational function to explain how the dosage a patient would need to achieve their original pain relief changes, given this diminished effectiveness.

Students will discuss how these forces explain the rise in heroin and fentanyl overdoses that plagues America today. Finally, they'll debate the responsibility that different parties should take in solving this epidemic.

Students will

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