In other words there was originally 4 parts per million Parentium-123 and 0 parts per million Daughterium-123.
Since there is now only 1/4 of the original amount of Parentium-123, we know that two half-lives of Parentium-123 have elapsed.
Say for example that a volcanic dike, or a fault, cuts across several sedimentary layers, or maybe through another volcanic rock type.
When ‘parent’ uranium-238 decays, for example, it produces subatomic particles, energy and ‘daughter’ lead-206.
Isotopes are important to geologists because each radioactive element decays at a constant rate, which is unique to that element.
We could be sure that a mineral containing parentium originally had no daughterium.
If the mineral contained 1 part per million Parentium-123 and 3 parts per million Daughterium-123, we could be sure all the Daughterium-123 was originally Parentium-123.
This decay is an example of an exponential decay, shown in the figure below.