## Math in radiocarbon dating

Exponential Decay Natasha Glydon Exponential decay is a particular form of a very rapid decrease in some quantity. One specific example of exponential decay is purified kerosene, used for jet fuel. The kerosene is purified by removing pollutants, using a clay filter.

If Po is the initial amount of pollutants in the kerosene, then the amount left, P, after n feet of pipe can be represented by the following equation: This means that we need a pipe that is Carbon 14 Dating Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material. The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.

Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.

At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues.

When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death. Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers.

The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay. In the case of radiocarbon dating, the half-life of carbon 14 is 5, years. This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50, years ago.

After 5, years, the amount of carbon 14 left in the body is half of the original amount. If the amount of carbon 14 is halved every 5, years, it will not take very long to reach an amount that is too small to analyze. When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is —0. How old is the fossil? We can use a formula for carbon 14 dating to find the answer.

So, the fossil is 8, years old, meaning the living organism died 8, years ago. Plutonium Plutonium is a man-made radioactive isotope. Plutonium is used to make nuclear explosives. Plutonium has a half-life of 24, years, which means that it would take , years to decay to a safe amount.

Plutonium decays exponentially into lead, but it causes concerns for humans because the tiny particles of plutonium react with oxygen and water and can be extremely flammable. Since the half-life of Plutonium is so high even in comparison to the carbon 14 half-life of 5, years humans must be very cautious of the way they dispose of plutonium.

Scientists are looking for safe ways for disposing plutonium. I am just learning the recipe so it takes me more time to look back and forth and double check. The more cookies I make, the more practice I have and the less time it takes me to bake the cookies. We can use exponential decay to represent a number of different things. Most importantly, exponential decay is not linear and the decrease is rapid at first, but not constant.

It is often used to describe population decreases or increases, which depicts exponential growth and can be seen using a graph of an exponential curve.