# Thread: logarithmic half life question

1. ## logarithmic half life question

Hi I'm new to this site so sorry if I've posted this in the wrong area, although this is part of my math12 curriculum.

If a 200g substance decays to 17g in 28 days, determine the half life of this substance.

The formula I came up with was this

17=200(1/2)^(x/28)

please tell me if this is correct or not.

Thank you very much.

2. Originally Posted by Jarsht
Hi I'm new to this site so sorry if I've posted this in the wrong area, although this is part of my math12 curriculum.

If a 200g substance decays to 17g in 28 days, determine the half life of this substance.

The formula I came up with was this

17=200(1/2)^(x/28)

please tell me if this is correct or not.

Thank you very much.
$\displaystyle A(t) = A_0e^{-\lambda t}$

$\displaystyle \lambda = \frac{ln(2)}{t_{1/2}}$

$\displaystyle A(t) = A_0e^{-\frac{t\,ln(2)}{t_{1/2}}}$

$\displaystyle 17 = 200e^{-\frac{28ln(2)}{t_{1/2}}}$

$\displaystyle -\frac{28ln(2)}{t_{1/2}} = ln \left(\frac{17}{200}\right)$

$\displaystyle t_{1/2} = -\frac{28ln(2)}{ln \left(\frac{17}{200}\right)}$

3. Thanks that's what I thought, props to you my fair scholar.