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Carbon dating formula example

Carbon 14 is a common form of carbon which decays over time.

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 two solutions provided differ slightly in their approach in this regard.

Scientists use a technique called radiometric dating to estimate the ages of rocks, fossils, and the earth.Many people have been led to believe that radiometric dating methods have proved the earth to be billions of years old.This has caused many in the church to reevaluate the biblical creation account, specifically the meaning of the word “day” in Genesis 1.With our focus on one particular form of radiometric dating—carbon dating—we will see that carbon dating strongly supports a young earth.Note that, contrary to a popular misconception, carbon dating is not used to date rocks at millions of years old.Before we get into the details of how radiometric dating methods are used, we need to review some preliminary concepts from chemistry.Recall that atoms are the basic building blocks of matter.Atoms are made up of much smaller particles called protons, neutrons, and electrons.Protons and neutrons make up the center (nucleus) of the atom, and electrons form shells around the nucleus.The number of protons in the nucleus of an atom determines the element.For example, all carbon atoms have 6 protons, all atoms of nitrogen have 7 protons, and all oxygen atoms have 8 protons.

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