The math behind radioactive isotope decay is very hard - I can't believe you are expected to do that.Hmmm....I thought it just decayed...The rate of decay reduces the amount of carbon which is measurable ~ which requires math I don't have.
Any exchange becomes a containment because different substances start with different amounts of carbon which decay @ different rates. Like I said...
I so appreciate that some people's minds work in ways that make sense of this stuff.
The radioactive carbon does just decay. But it keeps being replenished while the organism is alive because that organism takes it in from the environment (eg by eating it) and the radioactive carbon incorporates itself into that creature's body through what I think is isotopic exchange. So you can't tell the decay is happening while it is alive because there is always new 'fresh' radioactive carbon being brought on board.
But the minute the creature dies it takes no new radioactive carbon on board and then it is all about the decay math. I think the radioactivity level reduces to half in some impossibly long time - like thousands of years.