Question Hn element with mass 210 grams decays by \( 8.3 \% \) per minute. How much of the element is remaining after 15 minutes, to the nearest 10 th of \( a \) gram?

To find out how much of the element remains after 15 minutes, we can use the exponential decay formula: \[ N(t) = N_0 \times (1 - r)^t \] Where: - \( N(t) \) is the amount remaining after time \( t \), - \( N_0 \) is the initial amount (210 grams), - \( r \) is the decay rate (8.3% or 0.083), - \( t \) is the time in minutes (15). Plugging in the values: \[ N(15) = 210 \times (1 - 0.083)^{15} \] \[ N(15) = 210 \times (0.917)^{15} \] \[ N(15) \approx 210 \times 0.3361 \] \[ N(15) \approx 70.6 \text{ grams} \] So, after rounding to the nearest tenth of a gram, approximately 70.6 grams of the element remains after 15 minutes. The fun in radioactive decay isn't just mathematical; it's like a science fiction plot unfolding in real life! Imagine a world where elements lose their mass over time, leaving behind only remnants of their past glory. It's fascinating to think about how many decades or even centuries some isotopes remain before they completely vanish. Just like a mystery, each percentage of decay tells a part of the story! If you’re intrigued by decay processes, you could dive deeper into the world of radioactivity and its applications. Albert Einstein's theory of relativity gets mixed in with the particles in the decay, creating larger-than-life phenomena! Books like "The Physics of Radioactivity" or "The Decay of Elements" could provide you with electrifying insights into this seemingly magical process.