Question

An artifact was found and tested for its carbon-14 content. If 83% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

Answer 1

solve
\[.83=(\frac{1}{2})^{\frac{t}{5730}}\] for t

Answer 2

\[\frac{t}{5730}=\frac{\ln(.83)}{\ln(.5)}\]
\[t=\frac{5730\times \ln(.83)}{\ln(.5)}\]

Answer 3

idea is that to solve
\[b^x=A\] for x you use
\[x=\frac{\ln(A)}{\ln(b)}\]

Answer 4

I think I am supposed to find the answer in years, how is that answer found? I'm confused