The table illustrates the decay occurring in a 352-gram sample of vanadium-49 as time progresses.

Time (days) | Vanadium-49 (grams)
0 | 352
330 | 176
660 | 88
990 | 44
1,320 | X
Approximately how many grams of vanadium-49 will remain after a span of 1,320 days?

1 answer

The decay of vanadium-49 follows a pattern where it halves its quantity after every 330 days.

Let's break it down:

  • At 0 days, there are 352 grams.
  • After 330 days, the amount halves to 176 grams.
  • After another 330 days (660 days total), it halves again to 88 grams.
  • After another 330 days (990 days total), it halves once more to 44 grams.

Continuing this pattern, after an additional 330 days (which brings us to 1,320 days), we will halve the amount remaining at 990 days (44 grams):

\[ \text{Amount at 1,320 days} = \frac{44 \text{ grams}}{2} = 22 \text{ grams} \]

Thus, approximately 22 grams of vanadium-49 will remain after 1,320 days.