View Full Version : Half life equation math
stezza101
Aug 26, 2010, 05:17 PM
If I had 185 m&m's over a period of 10 hours predict the time when half the m&m's would be left using half life
JudyKayTee
Aug 26, 2010, 05:30 PM
Assuming this is homework, please post your answer and someone will come along to agree or disagree.
stezza101
Aug 26, 2010, 05:34 PM
Assuming this is homework, please post your answer and someone will come along to agree or disagree.
I got an equation t=L[ln(n/no)/Ln(1/2)]
but it makes no sense. Is the equation even correct?
ArcSine
Aug 27, 2010, 04:49 AM
A couple of equivalent approaches to solving for time t (which it appears you're shooting for), starting with the basic half-life relationship...
\frac{1}{2} \ = \ e^{-rt}\ \ \Longrightarrow \ \
ln\frac{1}{2} \ = \ -rt \ \ \Longrightarrow \ \
-\frac{ln\ 1/2}{r} \ = \ t
Or a slightly different route to the same destination...
\frac{1}{2} \ = \ (e^t)^{-r}\ \ \Longrightarrow\ \
\frac{1}{2}^{(-1/r)} \ = \ e^t \ \ \Longrightarrow \ \
\left(-\frac{1}{r}\right)ln\frac{1}{2} \ = \ -\frac{ln(1/2)}{r} \ = \ t
Hope that helped a bit. P.S.: Around my house M&Ms have a half-life measured in milliseconds.