Question

A fossilized animal that was killed by a volcanic eruption has 6.25 percent of its original amount of carbon-14 remaining; this radioisotope has a half life of 5730 years. How long ago did the volcano erupt?

Answer 1

Solution 1

\[6.25percent -> 0.0625 -> 1/16 -> (1/2)^4\]
Half life: 5730 years
Time = 5730*4 =22920

Solution 2

r: rate of carbon-14 diminishing
\[0.0625=r^t\]
\[0.5=r^{5730}\]\[r=0.5^{1/5730}\]
\[0.0625=(0.5^{1/5730})^t\]
\[log(1/16)=tlog(0.5^{1/5730})\]
\[t=log(1/16)/log(0.5^{1/5730})\]
22920