An artifact was found and tested for its carbon-14 content. If 82% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)

Question

anonymous · Answer

the equation for this is $$f=i(e ^{kt})$$
First you need to find the rate of decay (k).
Because half of it decays in 5730 years,  I can say 
$$50=100 e^{k(5730)}$$
so ln(1/2)=5730k
k=-1.209*10^-4

Using this k, you can find the answer

$$87=100e ^{-1.209*10^{-4}t}$$

solving this gives
$$ln(.87)={-1.209*10^{-4}t}$$
t=1151.878 years