Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.Consider some molten rock in which isotopes and elements are distributed in a reasonably homogeneous manner.The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.
It is not easily explained, in the general case, in any other way.
The data points would be expected to start out on a line if certain initial conditions were met.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age...
especially in absence of cross-checks by different methods, or if presented without sufficient information to judge the context in which it was obtained.
(Rocks which include several different minerals are excellent for this.) Each group of measurements is plotted as a data point on a graph.
The X-axis of the graph is the ratio of in a closed system over time.