document.write( "Question 1157950: The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of
\n" ); document.write( " Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists
\n" ); document.write( " conducted a chemical analysis of samples from the volcano area. The samples
\n" ); document.write( " contained approximately 62% of its original carbon-14. How long ago was the last
\n" ); document.write( " eruption of the volcano? Use 5730 years for the half-life of carbon-14.
\n" ); document.write( " Work must be shown!
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #780880 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "An equation of the radioactive decay in this case is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = ,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where C is the initial mass of carbon-14 in the sample; t is the time in years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve for \"t\", which is the major unknown in this case.\r\n" );
document.write( "\r\n" );
document.write( "Start canceling \"C\" in both sides.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     = 0.62\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Take logarithm base 2 from both sides\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    -t/5730 = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    -t/5730 = -0.6897\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    t = 5730*0.6897 = 3952 years    (rounded to closest integer value).      ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );