Question

The radioactive isotope carbon-14 has a half-life of 5730 years.

a) The decay constant of carbon-14 is:



b) If you have 65 grams of carbon-14 to begin with, the equation that describes the radioactive decay is
P(t) =

Answer 1

If you have a half-life, you can always say that the constant k in the equation y = ce^(kt) is \[\frac{ -\ln2 }{ half-life }\]Now, you may have seen the y=ce^(kt) formula written with different letters, but its the same formula. So since we always have that -ln2/half-life formula, we can get your constant
\[\frac{ -\ln2 }{ 5730 } \approx -.0001\]

The 2nd thing we need is that c in y = ce^(kt). That letter c is ALWAYS the same as the initial amount you have. Whatever amount you start with is what c equals. SO since your problem says you have 65g to begin with, c = 65, meaning you havethis equation:
\[y = 65e^{-.0001t}\]

Hope that helps some.