An element with mass 640 grams decays by 7.3% per minute. How much of the element is remaining after 8 minutes, to the nearest 10th of a gram?

Sure, here's how you can solve this problem:

Step 1: Convert the percentage decay per minute into a decimal. This is done by dividing the percentage by 100. So, 7.3% becomes 0.073.

Step 2: Determine the decay factor. This is done by subtracting the decimal form of the percentage decay from 1. So, 1 - 0.073 = 0.927. This means that each minute, 92.7% of the element remains.

Step 3: Apply the decay factor for each minute. Since the element decays for 8 minutes, you raise the decay factor to the power of 8. So, 0.927^8 = 0.557.

Step 4: Multiply the initial mass of the element by the decay factor after 8 minutes to find the remaining mass. So, 640 grams * 0.557 = 356.5 grams.

Therefore, to the nearest tenth of a gram, 356.5 grams of the element remains after 8 minutes.