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The same isotope system is used for each pair of samples, but the daughter to parent ratio is different in each sample.How would you use these data to calculate the geologic age indicated by the isotopes in each sample?For study purposes, some parts of the Grand Canyon stratigraphy are not shown in the diagram.The Precambrian strata have been reduced to a representative set of formations.You can use principles of relative geologic age to determine sequences of geologic events, including rock formations, intervals of erosion, tilting, folding, and faulting like those represented in the block diagrams and cross-sections below.Be sure to review the principles of relative geologic age on the Geologic Time Basics page .An isotope system is assumed to be a closed system with regard to the parent and daughter - they remain within the system and do not leave it, and at the same time no isotopes of the parent or daughter type enter the system from outside.
The mathematical formula is expressed as follows: where age is the absolute age (typically using years as the time unit), ln is the natural logarithm, D is the amount of daughter isotope, and P is the amount of parent isotope.
By the definition of a half-life, the amount of parent isotope at each half-life is half of what it was before the half-life elapsed.
As the amount of parent isotope decreases by radioactive decay, the amount of the daughter isotope increases commensurately.
The table below tracks the decay, half-life by half-life, of a radioactive isotope, and the accumulation of the daughter product isotope that the parent changes into once it decays. There are several different radioactive isotope systems that are used for measuring ages of geologic materials.
For more information on these systems, see the isotopes and half-lives section of the Geologic Time Basics page.