Question 7 A radioactive compound with mass 320 grams decays at a rate of \( 27 \% \) per hour. Which equation represents how many grams of the compound will remain after 7 hours? Answer

To find the amount of a radioactive compound remaining after a specific period, we can use the formula for exponential decay. Since the compound decays at a rate of \( 27 \% \) per hour, we can express the remaining mass after \( t \) hours as: \[ M(t) = M_0 (1 - r)^t \] Where \( M_0 \) is the initial mass (320 grams), \( r \) is the decay rate (0.27), and \( t \) is the time in hours. Plugging in the values, we get: \[ M(7) = 320 (1 - 0.27)^7 \] Which simplifies to: \[ M(7) = 320 (0.73)^7 \] After 7 hours, this equation tells us how much of the radioactive compound remains. If you have further questions or you'd like to explore this topic, you could think about how this type of decay is crucial in fields like nuclear medicine or archaeology, where understanding the half-life of substances can lead to groundbreaking discoveries! Plus, it's fascinating to see how exponential decay spills into everyday life, like in the diminishing brightness of a glowing stick or the cooling of a hot cup of coffee!