A radionctive compound with mass 320 grams decays at a rate of \( 27 \% \) per hour. Which equation represents how many grams of the compound will remain atter 7 hours? Answer \( \begin{array}{l}C=320(1+0.27)^{7} \\ C=320(0.27)^{7} \\ C=320(1.27)^{7} \\ C=320(1-0.27)^{7}\end{array} \)

To determine how many grams of the compound will remain after 7 hours, you need to apply the principles of exponential decay because the radioactive substance decays over time. The correct formula to represent this scenario is based on the initial mass and the decay rate. You’d suck out the percentage that remains after each hour, leading us to use \( (1 - 0.27) \) to show that only \( 73\% \) of the mass remains each hour. So the equation is \( C = 320(1 - 0.27)^{7} \). In real-world terms, this kind of decay is similar to what happens with various substances in nature, including elements like Carbon-14 used in dating ancient artifacts. By using the radioactive decay formula, scientists can estimate the age of organic materials based on the remaining amount of these isotopes, making it an essential tool in archaeology and geology!