# Carbon dating problems calculus

This means A can be replaced with .2Ao (20% of the original).Replacing A with .2 Ao and solving for t we get: Math works just like anything else, if you want to get good at it, then you need to practice it.

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.

The decay model describes the amount of carbon-14 present after t years.

How many grams of carbon-14 will be present in this artifact after 10,000 years?

Plugging in 10000 for t and solving for A we get: : A certain radioactive isotope element decays exponentially according to the model , where A is the number of grams of the isotope at the end of t days and Ao is the number of grams present initially. If we are looking for the half-life of this isotope, what variable are we seeking? It looks like we don’t have any values to plug into A or Ao.

However, the problem did say that we were interested in the HALF-life, which would mean ½ of the initial amount (Ao) would be present at the end (A) of that time. Replacing A with .5 Ao and solving for t we get: : Prehistoric cave paintings were discovered in a cave in Egypt. Using the exponential decay model for carbon-14, , estimate the age of the paintings.Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument.To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem.Since we are looking for the age of the paintings, what variable are we looking for? It looks like we don’t have any values to plug into A or Ao.However, the problem did say that the paintings that were found contained 20% of the original carbon-14.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?

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