document.write( "Question 1149491: In order to determine the age of a piece of wood, the amount of carbon-14 was measured. It was determined that the wood had lost 33.1% of its carbon-14. How old is this piece of wood? \n" ); document.write( "

Algebra.Com's Answer #770826 by ikleyn(52770) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Carbon (C) has three naturally occurring isotopes. Both C-12 and C-13 are stable, but C-14 is radioactive
\n" ); document.write( "and decays to nitrogen-14 with a half-life of approximately 5,730 years. Naturally occurring radiocarbon is
\n" ); document.write( "produced as a secondary effect of cosmic-ray bombardment of the upper atmosphere. Plants transpire
\n" ); document.write( "to take in atmospheric carbon, which is the beginning of absorption of carbon into the food chain. \r
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\n" ); document.write( "\n" ); document.write( "As long as the plant is alive, the ratio of C-14 to C-12 in its body remains constant.
\n" ); document.write( "After the plant dies, carbon-14 continues to decay without being replaced.\r
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\n" ); document.write( "\n" ); document.write( "The current amount of radioactive Carbon-14 present in the remains of the plant can be measured,
\n" ); document.write( "and the ratio of the current amount of Carbon-14 to its initial amount can be used to determine age.
\n" ); document.write( "The last ratio is described by the function C(t) = 0.5^(t/5730), where \"t\" is time (in years).\r
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document.write( "     Since 33.1% of Carbon-14 is lost, 66.9% is remained, or 0.669 of its initial amount.\r\n" );
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document.write( "     Thus, you should solve an equation C(t) = 0.669, which is  y =  = , for unknown t. \r\n" );
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document.write( "     Take logarithm base 10 from both sides. You get an equation  = .\r\n" );
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document.write( "     Apply the Power Rule to the logarithm. You get an equation .\r\n" );
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document.write( "     Therefore,  =  = 3323 years.\r\n" );
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document.write( "    ANSWER.  The piece of wood is about 3323 years old.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The letter which you see cut in all formulas, is the letter \"t\", symbolizing time.\r
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\n" ); document.write( "\n" ); document.write( "There is a group of lessons in this site, which covers all these and similar problems\r
\n" ); document.write( "\n" ); document.write( "    - Using logarithms to solve real world problems, and\r
\n" ); document.write( "\n" ); document.write( "    - Solving problem on Newton Law of cooling \r
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\n" ); document.write( "\n" ); document.write( "So, if somebody wants to learn on how to solve such problem, he (or she) has good source to read from.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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