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:
[tex]A=Pe^{rt} [/tex] 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:
[tex]A=32e ^{(-.00012)(4300)} [/tex]
First thing to do is to simplify that multiplication involving the exponents. Doing that gives us:
[tex]A=32e ^{-.516} [/tex]
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:
[tex]e ^{(} [/tex]
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.
