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# A piece of bone of an animal from a ruin is found to have $\;^{14}C\;$ activity of 12 disintegrations per minute per gm of its carbon content .The $\;^{14}C\;$ activity of a living animal is 16 disintegrations per minute per gm .How long ago nearly did the animal die ? (Given half life of $\;^{14}C\;$ is $\;t_{\large\frac{1}{2}}\;$=5760 years)

$(a)\;1672\;years \qquad(b)\;2391\;years \qquad(c)\;3291\;years \qquad(d)\;4453\;years$

12/16 = (1/2)^(t/5760

log(3/4) = -(t/5760)(log2)

log3-2log2 = (t/5760)log2

t=2390.61 which is nearly equal to 2391 years