# Exponential and logarithmic functions in carbon 14 dating

If you need a review on these topics, feel free to go to Tutorial 42: Exponential Functions and Tutorial 45: Exponential Equations. For example, if the model is set up at an initial year of 2000 and you need to find out what the value is in the year 2010, t would be 2010 - 2000 = 10 years.

You can use this formula to find any of its variables, depending on the information given and what is being asked in a problem.

This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.

A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the \$-0.693\$ value, but perhaps my answer will help anyway.

Some examples of exponential growth are population growth and financial growth.

Plugging in 60 for A and solving for t we get: Since we are looking for when, what variable do we need to find? What are we going to plug in for A in this problem? Plugging 200000 for A in the model we get: t is the amount of time that has past.As mentioned above, in the general growth formula, k is a constant that represents the growth rate. Since we are looking for the population, what variable are we finding? What are we going to plug in for t in this problem?Our initial year is 1994, and since t represents years after 1994, we can get t from 2005 - 1994, which would be 11.Or you can use it to find out how long it would take to get to a certain population or value on your house.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. However, I note that there is no beginning or ending amount given.