Question 1136372
<br>
The fraction of the material remaining after n half-lives is<br>
{{{(.5)^(n)}}}<br>
(a) Determine the half-life<br>
In this problem, the amount of material decreased by 51% in 560 days; that means after 560 days 49% remains.  Use the basic formula to determine how many half-lives that is.<br>
{{{(.5)^n = 0.49}}}
n = 1.0291463  (to several decimal places, using a graphing calculator)<br>
So the half-life of the material is<br>
{{{560/1.0291463 = 544.14}}}<br>
(b) Determine how long it will take a 100mg sample to decay to 47mg<br>
Use the basic formula to determine the number of half-lives it takes for the material to decay to where 47% remains, then multiply the half-life by that number.<br>
{{{(.5)^n = 0.47}}}
{{{n = 1.0892673}}}
{{{1.0892673*544.14 = 592.7139}}}<br>
It takes about 593 days for a 100mg sample to decay to 47mg.