Half life represents the time period after which a substance will lose half of its original content. Thus, in the given example, half of the starting amount of iodine-131 will be left after 8.03 days. In another 8.03 days (that is, after 16.06 days from start), another 50% will be lost. We will, effectively, be left with only 25% of the original content.

In 38 days, 38/8.03 = 4.79 half lives would have been gone.

The amount of a material left, after a certain number of half lives can be calculated as:

Nt/N0 = 1/{(2)^(t/t1/2)}

where, t1/2 is half live and t/t1/2 is the number of half lives elapsed.

Thus, the fraction iodine-131 left after 4.79 half lives is:

Nt/N0 = 1/(2^4.79) = 0.036.

Thus, only 0.036 or 3.6% fraction of iodine-131 would be left after 38.5 days.

Hope this helps.

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