# logarithmic half life question

• Oct 25th 2009, 01:23 PM
Jarsht
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.

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

please tell me if this is correct or not.

Thank you very much.
• Oct 25th 2009, 01:31 PM
e^(i*pi)
Quote:

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.

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

please tell me if this is correct or not.

Thank you very much.

$A(t) = A_0e^{-\lambda t}$

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

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

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

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

$t_{1/2} = -\frac{28ln(2)}{ln \left(\frac{17}{200}\right)}$
• Oct 25th 2009, 01:33 PM
Jarsht
Thanks that's what I thought, props to you my fair scholar.