# Exponential and logarithmic functions in carbon 14 dating

In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 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 50,000 years ago.

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.

Our initial year is 1994, and since t represents years after 1994, we can get t from 2005 - 1994, which would be 11.

Plugging in 11 for t and solving for A we get: Looks like we have a little twist here.

The diagram below shows exponential growth:: The exponential growth model describes the population of a city in the United States, in thousands, t years after 1994.

Use this model to solve the following: A) What was the population of the city in 1994?

This happens to be the number in front of e which is 30 in this problem.

The reason I showed you using the formula was to get you use to it.

Now we are given the population and we need to first find t to find out how many years after 1994 we are talking about and then convert that knowledge into the actual year.

We will still be using the same formula we did to answer the questions above, we will just be using it to find a different variable.

So, the fossil is 8,680 years old, meaning the living organism died 8,680 years ago.

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