document.write( "Question 1158200: The amount of carbon-14 in an object is given by y=a e^-0.00012 t, where a is the amount of carbon-14 originally in the object, and t is the age of the object in years. A fossil bone contains 18% of its original carbon-14. What is the approximate age of the bone? \n" ); document.write( "

Algebra.Com's Answer #781097 by Shin123(626) $\"\"$ $\"About$

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There used to be $\"a\"$ carbon-14 but now there is only 0.18a carbon-14. So $\"e%5E%28-0.00012t%29=0.18\"$ . Taking the natural logarithm of both sides gives $\"-0.00012t=ln%280.18%29\"$ Dividing both sides by -0.00012 gives $\"t=-ln%280.18%29%2F0.00012\"$ Since $\"ln%280.18%29\"$ is about -1.7148, we have $\"t=1.7148%2F0.00012=14290\"$ years old. \n" ); document.write( "

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