Assume that you have a large sample of radioactive atoms, arranged in a rectangular lattice. Imagine that this lattice has some
number of rows and columns, with an atom in each lattice-position. Now, in this scenario, the atoms do *NOT* decay independently. Instead, each row and column of atoms decays independently. More specifically, imagine that each row of atoms decays as a random variable, independently of all other rows and columns. Say that the probability of any particular row decaying over the course of one hour is 10%. In addition, each column of atoms decays as a random variable, independently of all other rows and columns
Say that the probability of any particular column decaying over the course of one hour is 40%.
Can you make a model for how the total number of atoms decays?
Make a graph/plot of your model, illustrating the amount of radioactive material you expect as a function of time in hours).
Does the total number of atoms decay exponentially?
If so, can you define a decay rate for the total number of atoms?
