The "active" in "radioactive" means that unstable substances produced in nuclear reactions break down and change, so that they eventually become stable and no longer release radiation. The rate of breakdown can occur quickly in some radioactive substances, often within a few days. Half of the I-131 released during each atomic bomb test was gone in about 8 days. Almost all of it was gone (less than 1 percent remained) 80 days after the test.
Like all radioactive substances, I-131 releases radiation as it breaks down. It is this radiation that can injure human tissues. But I-131's steady breakdown means that the amount of I-131 present in the environment after a bomb test steadily decreased. Therefore, farm animals that grazed in fields within a few days after a test would have consumed higher levels of I-131 than animals grazing later.