Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.
For example, say a fossil is found that has 35% carbon 14 compared to the living sample. We can use a formula for carbon 14 dating to find the answer.
Where t is the age of the fossil (or the date of death) and ln() is the natural logarithm function.
The two solutions provided differ slightly in their approach in this regard.
Carbon dating has given archeologists a more accurate method by which they can determine the age of ancient artifacts.
$$ Time in this equation is measured in years from the moment when the plant dies ($t = 0$) and the amount of Carbon 14 remaining in the preserved plant is measured in micrograms (a microgram is one millionth of a gram).
So when $t = 0$ the plant contains 10 micrograms of Carbon 14.
They have their work cut out for them, however, because radiocarbon (C-14) dating is one of the most reliable of all the radiometric dating methods.
This article will answer several of the most common creationist attacks on carbon-14 dating, using the question-answer format that has proved so useful to lecturers and debaters. Answer: Cosmic rays in the upper atmosphere are constantly converting the isotope nitrogen-14 (N-14) into carbon-14 (C-14 or radiocarbon).
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.
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.