document.write( "Question 1202012: If 80% of a radioactive element remains radioactive after 200 million years, then what percent remains radioactive after 700 million years? What is the half life of this element? \n" ); document.write( "

Algebra.Com's Answer #836641 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "For the first question, note that we do not have to determine the half life of the element.

\n" ); document.write( "We know that after 200 million years 80% or 0.8 of the original amount remains. 700 million years is 3.5 times as long, so the fraction remaining after 700 million years is (0.8)^(3.5) = 0.45795 to 5 decimal places.

\n" ); document.write( "1st ANSWER: Approximately 45.795% remains after 700 million years

\n" ); document.write( "(NOTE! Since radioactive decay is a statistical process and not a smooth mathematical process, keeping that many significant digits in the answer is probably unrealistic....)

\n" ); document.write( "For the second question, to find the half life, we can start by determining after how many half lives 80% of the original amount remains.

\n" ); document.write( " $\"%281%2F2%29%5Ex=4%2F5\"$
\n" ); document.write( " $\"%28.5%29%5Ex=.8\"$
\n" ); document.write( " $\"x%2Alog%28.5%29=log%28.8%29\"$
\n" ); document.write( " $\"x=log%28.8%29%2Flog%28.5%29\"$

\n" ); document.write( "To several decimal places, that is 0.321928.

\n" ); document.write( "Then, since 80% remains after 200 million years, the half life in millions of years is

\n" ); document.write( "200/0.321928 = 621.257 to a few decimal places.

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

\n" );