Question 1195957
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The fraction of carbon-14 remaining after n half-lives is {{{(1/2)^n}}}.  Use that formula to determine the number half-lives.<br>
{{{(0.5)^n=0.76}}}<br>
The variable is in an exponent, so use logarithms.<br>
{{{log((0.5)^n)=log(0.76)}}}
{{{n*log(0.5)=log(0.76)}}}
{{{n=log(0.76)/log(0.5)}}} = 0.396 to 3 decimal places<br>
Multiply the number of half-lives by the number of years in a half-life.<br>
{{{0.396(5740)=2269}}}<br>
ANSWER: The age of the Dead Sea Scrolls is about 2269 years.<br>
Note that, as the problem says, this is an ESTIMATE of the age of the scrolls.<br>
Radioactive decay is a statistical process; the rate of decay is not absolutely constant.  So any calculation of the age of an object using carbon-14 dating only gives an approximate answer.  So this is an example of a calculation where you do NOT want to keep a large number of decimal places in your calculations.<br>
I found one internet source that says if the age is between 1000 and 10,000 years the convention is to round the age to the nearest 10.  So the best answer to this problem is that the age is ABOUT 2270 years.<br>