<PRE><B>Question 275217</B>
to the nearest full day determine how long it will take for 400 millicuries of I-131, which has a half life of 8 days, to decay to 3.125 millicuries?
:
The half-life equation  Ao*2^(-t/h) = A
Where
A = resulting amt 
Ao = initial amt
t = time (in days in this application)
h = half-life of the substance 
:
400 * 2^(-t/8) = 3.125
Divide both sides by 400
2^(-t/8) = {{{3.125/400}}}
2^(-t/8) = .0078125
:
ln(2^(-t/8)) = ln(.0078125)
:
{{{-t/8}}}*ln(2) = ln(.0078125)
{{{-t/8}}} = {{{(ln(.0078125))/(ln(2))}}}; enter in your calc
{{{-t/8}}} = -7
t = -7 * -8
t = 56 days
;
:
Check this on a calc: enter 400 * 2^(-56/7) results: 3.125
</PRE>