Ask Me Help Desk - Half life equation math

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

Assuming this is homework, please post your answer and someone will come along to agree or disagree.

Quote:

Originally Posted by JudyKayTee

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?

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.