Question 1152999
A wooden artifact from an archaeological dig contains 80 percent of the Carbon-14 that is present in living trees.
To the nearest year, about how many years old is the artifact?
 (The half-life of Carbon-14 is 5730 years.)
:
The radiation decay formula
{{{A = Ao*2^(-t/h)}}}, where
A = resulting amt after t time
Ao = initial amt of the substance
t = time of decay
h = half-life of substance
:
let Ao = 10 and A = 8
:
{{{10*2^(-t/5730) = 8}}}; (t is the numerator)
{{{2^(-t/5730) = 8/10}}}
{{{2^(-t/5730) = .8}}}
using natural logs
{{{-t/5730}}}ln(2) = ln(.8)
{{{(-t/5730) = ln(.8)/ln(2)}}}
using your calc
{{{(-t/5730) = -.3219}}}
t = -5730 * -3219
t = 1845 yrs