magazine has been continuously published since 1978, we are publishing some of the articles from the archives for historical interest, such as this.
Carbon dating model
The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained.
Research has been ongoing since the 1960s to determine what the proportion of in the atmosphere has been over the past fifty thousand years.
The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.
Students should be guided to recognize the use of the logarithm when the exponential function has the given base of $e$, as in this problem.
Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.
The standards do not prescribe that students use or know with log identities, which form the basis for the "take the logarithm of both sides" approach.
The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire in a sample from a dead plant or animal such as a piece of wood or a fragment of bone provides information that can be used to calculate when the animal or plant died.
The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.
The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age.