To determine the quantity of element X left after a certain period, we can use the concept of half-lives. The half-life is the time it takes for half of the substance to decay.
In this case, element X has a half-life of 5 days. Starting with 100 grams, we can calculate how much of it will remain after 10 days.
First, calculate how many half-lives have passed in 10 days:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{10 \text{ days}}{5 \text{ days}} = 2 \]
After each half-life, the amount of substance is halved. So, we can calculate the remaining quantity of element X after 2 half-lives as follows:
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After the first half-life (5 days): \[ \text{Remaining quantity} = \frac{100 \text{ grams}}{2} = 50 \text{ grams} \]
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After the second half-life (10 days): \[ \text{Remaining quantity} = \frac{50 \text{ grams}}{2} = 25 \text{ grams} \]
Therefore, after 10 days, the quantity of element X remaining is 25 grams.
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