Final answer:
To find the remaining Hogwartium after 500 years, we use the exponential decay formula based on its half-life of 713 years. The calculation results in approximately 49,672 grams, which suggests there might be an error in the provided answer choices.
Step-by-step explanation:
To calculate the remaining amount of Hogwartium after 500 years, given its half-life of 713 years, we apply the formula for exponential decay:
\[ \text{Remaining amount} = \text{initial amount} \times \left(\frac{1}{2}\right)^{\frac{\text{time}}{\text{half-life}}} \]
In this case, the initial amount is 62,442 grams, and we are interested in the amount left after 500 years. Plugging the values into the formula, we get:
\[ \text{Remaining amount} = 62,442 \times \left(\frac{1}{2}\right)^{\frac{500}{713}} \]
Using a calculator, we find that the remaining amount of Hogwartium is approximately:
\[ \text{Remaining amount} = 62,442 \times 0.7962 \approx 49,672 \text{ grams} \]
Rounded to the nearest gram, the remaining amount is 49,672 grams, which is not any of the options provided in the problem. This likely indicates that there was either a mistake in the problem setup or in the options given. It's important to revisit the problem and verify the provided options.