To determine the value of \( X \) in the given table regarding the degradation of a 420-gram seaborgium-266 sample, we can observe the pattern of the decay over the provided time intervals.
The table shows the following data:
- At 0 seconds, the mass is 420 grams.
- At 30 seconds, the mass is 210 grams, which is half of 420 grams.
- At 60 seconds, the mass is 105 grams, which is half of 210 grams.
This indicates that seaborgium-266 is undergoing exponential decay and has a half-life of 30 seconds. Therefore, we can predict the mass at \( 90 \) seconds.
Continuing this pattern:
- At 90 seconds, it would be half of 105 grams:
\[ X = \frac{105}{2} = 52.5 \text{ grams} \]
Thus, the value of \( X \) at 90 seconds is \( 52.5 \) grams.
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