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 week is 20%.

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 week 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 weeks).

Does the total number of atoms decay exponentially?

If so, can you define a decay rate for the total number of atoms?