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Carbon Dating Carbon$-14({?}^{14}C)$ dating assumes that the carbon dioxide on the Earth today has the same radioactive content as it did centuries ago. If this is true, then the amount of ${?}^{14}C$ absorbed by a tree that grew several centuries ago should be the same as the amount of ${?}^{14}C$ absorbed by a similar tree today. A piece of ancient charcoal contains only $14\%$ as much of the radioactive carbon as a plece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? $($The half$-$life of ${?}^{14}C$ is $5715$ years. Round your answer to one decimal place.$)$

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