Half-life of carbon-14 is 5730 years. A piece of wood that contained 0.200g of Carbon-14 when it was alive now contains 0.0125g of Carbon-14. How old is the piece of wood? 5730 years old 11460 years old 17190 years old 22920 years old?

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Answer 1 · 2016-09-11T19:48:08

22920

${(\frac{1}{2})}^{\frac{t}{5730}} (I) = A$ $(1/2)^(t/5730)(I)=A$

I = initial amount, A = current amount, t = years

I=0.200g, A= 0.0125g, solve for t

${(\frac{1}{2})}^{\frac{t}{5730}} (0.200) = 0.0125$ $(1/2)^(t/5730)(0.200)=0.0125$

${(\frac{1}{2})}^{\frac{t}{5730}} = 0.625$ $(1/2)^(t/5730)=0.625$

${log}_{\frac{1}{2}} ({(\frac{1}{2})}^{\frac{t}{5730}}) = {log}_{\frac{1}{2}} 0.0625$ $log_(1/2)((1/2)^(t/5730))=log_(1/2)0.0625$

$\frac{t}{5730} = 4$ $t/5730=4$

$t = 22920$ $t=22920$