Question 1202012
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For the first question, note that we do not have to determine the half life of the element.<br>
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.<br>
1st ANSWER: Approximately 45.795% remains after 700 million years<br>
(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....)<br>
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.<br>
{{{(1/2)^x=4/5}}}
{{{(.5)^x=.8}}}
{{{x*log(.5)=log(.8)}}}
{{{x=log(.8)/log(.5)}}}<br>
To several decimal places, that is 0.321928.<br>
Then, since 80% remains after 200 million years, the half life in millions of years is<br>
200/0.321928 = 621.257 to a few decimal places.<br>