Radiation Decay: Calculating Half-Life & Nuclei Activity

[Michael1974]

1. If I throw sixty different dice (compared to an atomic nucleus) and each dice that gets a 3 is disintegrated and disappear before the next roll. Altogether I make ten roll, where each roll corresponds to one day. The result is illustrated in a graph: http://imgur.com/TbXF4mf click on the picture to see. X = time in days, Y = decays under a day These questions must be answered: a) How can I read and calculate the half-life through my function expression? b) What is the function expression? c) the relationship between nuclei activity d) The difference between a nucleus and dice?2. No equations given.3. The half-life must surely be somewhere between the third and fourth day (throw). But how can I calculate it exactly by reading? Functional expression is well in my graph: 15.19 * e ^ -0,25x. This is indeed a exponentiellfunktion, if I understand correctly? How can I get out activity between nuclei I have not decay constant? The last question I do not understand at all ..

 

[haruspex]

how can I calculate it exactly by reading?

I believe the usual approach is maximum likelihood. I.e., what value of the parameter makes the observations most likely?
See e.g. https://en.wikipedia.org/wiki/Exponential_distribution.

Not sure that I understand the model, though.

sixty different dice (compared to an atomic nucleus)

Are you saying 60 dice represent (the neutrons in?) one nucleus? If so, once one has decayed everything changes. So I would have thought 60 dice represented 60 nuclei. Presumably, as they decay, you roll fewer dice each day.