# Carbon dating problems calculus

For example, you may be given the values for Ao and t and you need to find the amount A after the given time.

Or, you may be given the final amount A and the initial amount Ao and you need to find the time t.

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

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.

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.

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.

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.

Or you can use it to find out how long it would take to get to a certain population or value on your house.

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