A certain radioactive substance decays exponentially. If its half-life is 3 years and its initial mass is 200 grams, how much will remain after 9 years?

Sat, 02 May 2026 17:03:20 +0000

**A certain radioactive substance decays exponentially. If its half-life is 3 years and its initial mass is 200 grams, how much will remain after 9 years?** In a world increasingly shaped by precise scientific understanding, curiosity about how matter changes over time deepens our connection to fundamental natural processes—ones that influence medicine, energy, and environmental awareness. One such process centers on a certain radioactive substance that decays exponentially. At first glance, this may sound abstract—but tracking its remaining mass after 9 years reveals clarity, practicality, and an enduring lesson in exponential behavior. When a small 200-gram sample undergoes radioactive decay with a half-life of just 3 years, only 25 grams remain after 9 years—a result grounded in math, validated by science, and increasingly relevant in real-world applications. This is not just a number; it’s a story of predictable transformation. Why is this decay model gaining attention across the U.S. in educational, technical, and public discourse? Across fields such as nuclear medicine, environmental cleanup, and scientific literacy, exponential decay offers a powerful lens for understanding change. Data trends show growing public interest in microbial and nuclear sciences, driven by expanding clean energy initiatives and advancements in medical imaging technologies like PET scans. The ability of a certain radioactive substance to halve every 3 years reflects a natural rhythm that’s both simple and profound—a rhythm users now seek to understand for personal curiosity, academic learning, and professional insight. To grasp how much remains after 9 years, consider the core principle: exponential decay follows a mathematical pattern tied directly to the half-life. Half-life—the time it takes for half the original amount to transform—unlocks immediate clarity. Since the half-life here is