An artifact was found to have an original amount of carbon-14 of 32 grams. approximately how many grams of carbon-14 remain after 4300 years? carbon 14 decays at a rate of -0.00012 grams per year.
9.6 grams
19.1 grams
22.4 grams
31.2 grams

The formula used for this is the same one used to find interest accrued in a bank account that compounds continuously.  The only difference is that our r here, the rate, is a negative number because the carbon is deteriorating over time, whereas money grows over time.  That formula is this one:
where A is what's left in the end, P is the initial amount of carbon, r is the rate at which it deteriorates (sometimes a k in other formulas, but same thing!) and t is the time in years.  For us, that formula, filled in, looks like this:

First thing to do is to simplify that multiplication involving the exponents.  Doing that gives us:

On your calculator, you have a 2nd button and an LN button.  If you push 2nd and then LN you get this in your display:

and it's up to you to add the exponent on the e.  Our exponent is the -.516. So do that and then multiply that result by 32 to get that your answer is 19.1 g of carbon remaining.

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