When nuclei decay, we can plot a graph to show how the number of undecayed nuclei changes with time. It’s very predictable, different for each isotope, but the graph is a very particular shape, called an exponential. Notice, the shapes are similar.
Imagine a very infectious, fatal disease. In the first day, 100,000 people catch it and die, in the second day, 50,000, the third day 25,000. Less people die because there are less people alive to catch the disease. As time goes on, less nuclei decay because there are less available to decay.
We can show this on a graph, measuring the count rate from a detector and plotting it against time. Some schools have a Thorium cow which can be ‘milked’ to measure the decay of gaseous radioactive Radon, one of its daughter products, as Radon decays by alpha decay into Polonium 216.
Here’s a game to play. Take 100 dice. Imagine that if you throw a six the dice has ‘decayed’. Throw all the dice and take away and all the sixes. Put them on one side, count the ones that are left and throw again with the number left. Repeat several times, or until there are very few ‘undecayed’ dice left. Plot the number left against the number of goes. The graph looks just like a decay curve. We have no idea which dice will ‘decay’ but we can predict when roughly half of them have.