A radioactive substance decays exponentially, with a half-life of 3 years. Starting with 1,000 grams, how many grams remain after 9 years?

Wed, 29 Apr 2026 17:21:33 +0000

**How A Radioactive Substance Decays Exponentially—With 1,000 Grams Over 9 Years** Ever wondered how long a radioactive material truly lasts? One classic example is a substance decaying with a half-life of 3 years—meaning its amount halves every three years. Starting with 1,000 grams, a simple question emerges: How many grams remain after 9 years? This isn’t just a math riddle—it’s a conversation starter in science, safety, and even emerging tech. With growing interest in nuclear energy, medical isotopes, and environmental tracking, understanding exponential decay matters more than ever. Let’s break it down in a clear, stable way. ### Why A Radioactive Substance Decays Exponentially, With a Half-Life of 3 Years. Starting with 1,000 grams, How Many Grams Remain After 9 Years? Radioactive decay follows a precise, mathematical pattern rooted in physics. At its core, half-life defines the time it takes for half the original amount to transform. With a 3-year half-life, the decay happens in distinct, predictable intervals. This isn’t just a theoretical concept—predictable decay rates are vital for medical diagnostics, nuclear energy management, and environmental safety. The formula linking initial mass, half-life, and elapsed time works powerfully here, offering a simple path to clarity.