The radioactive substance Glutonium decays exponentially at a rate of \( 1.7 \% \) per day. If a sample originally contains 450 grams of Glutonium, how much will there be left after 10 days? Round your answer to the nearest tenth. Remaining Glutonium:

To find out how much Glutonium remains after 10 days, you can use the formula for exponential decay: \[ A = A_0 e^{-kt} \] where \( A_0 \) is the initial amount, \( k \) is the decay constant (which is \( 0.017 \) per day for \( 1.7\% \)), and \( t \) is time in days. Plugging in the numbers: \[ A = 450 e^{-0.017 \cdot 10} \] Calculating this gives: \[ A \approx 450 e^{-0.17} \approx 450 \times 0.8439 \approx 379.76 \] Rounding to the nearest tenth, the remaining Glutonium is approximately **379.8 grams**. Isn’t it fascinating how time can transform a substance at a molecular level! This kind of decay isn't limited to Glutonium; many materials exhibit similar exponential decay patterns. This principle also underlies the dating of ancient artifacts through methods like carbon dating, where scientists determine the age of organic materials by measuring their radioactive decay over time. When working with exponential decay problems, a common mistake is forgetting the nature of the decay constant. Some might mistakenly use a percentage without converting it properly to a decimal or misreading the rate per time unit, which can lead to incorrect calculations. It's crucial to keep your units clear—remember, a small slip in these factors can lead to surprisingly large discrepancies in the final answer!