In order to use these methods, we have to start out with a system in which no daughter element is present, or else know how much daugher element was present initially so that it can be subtracted out.
We also need to know that no parent or daughter has entered or left the system in the meantime.
Assuming we start out with pure parent, as time passes, more and more daughter will be produced. A ratio of infinity (that is, all daughter and no parent) means an age of essentially infinity.
By measuring the ratio of daughter to parent, we can measure how old the sample is. Each radioactive element has a half-life, which tells how long it takes for half of the element to decay.
For potassium 40, the half-life is about 1.3 billion years.