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.
The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.
The equation is the one which describes radioactive decay: If one of these assumptions has been violated, the simple computation above yields an incorrect age.
These changes typically occur so slowly that they are barely detectable over the span of a human life, yet even at this instant, the Earth's surface is moving and changing.
As these changes have occurred, organisms have evolved, and remnants of some have been preserved as fossils.
Isochron methods avoid the problems which can potentially result from both of the above assumptions.