document.write( "Question 62160: I am having trouble with this one. Anyone out there that can help me. Thanks!\r
\n" ); document.write( "\n" ); document.write( "The half-life of radioactive carbon-14 is 5,700 years. How much initial sample will remain after 3,000 years. \r
\n" ); document.write( "\n" ); document.write( "Thanks!
\n" ); document.write( "

Algebra.Com's Answer #42926 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The half-life of radioactive carbon-14 is 5,700 years. How much initial sample will remain after 3,000 years.
\n" ); document.write( ":
\n" ); document.write( "The half-life formula that I have:
\n" ); document.write( ":
\n" ); document.write( "A = Ao[.5^(t/h)]
\n" ); document.write( "Where:
\n" ); document.write( "Ao = initial amt
\n" ); document.write( "t = time (yrs here)
\n" ); document.write( "h = half life of the substance
\n" ); document.write( ":
\n" ); document.write( "Let the initial sample (Ao) = 1, t = 3000, h = 5700
\n" ); document.write( ":
\n" ); document.write( "A = 1*(.5^(3000/5700))
\n" ); document.write( "A = .5^.5263
\n" ); document.write( "ln(A) = .5263*ln(.5); using nat logs
\n" ); document.write( "ln(A) = -.3648
\n" ); document.write( "A = .6943
\n" ); document.write( ":
\n" ); document.write( "We can say that 69.43% of the initial amt remain after 3000 years\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );