# half life of a decay process

• Feb 15th 2008, 05:22 PM
icetea
half life of a decay process
hi im new =)
i need help with this question..

Question:
An exponential decay curve passes through the points (3, 560) ad (7, 280)

a)What is the half life of this decay process?
b)What is the initial value of the quantity being measured?

thanks alot
• Feb 15th 2008, 06:36 PM
mr fantastic
Quote:

Originally Posted by icetea
hi im new =)
i need help with this question..

Question:
An exponential decay curve passes through the points (3, 560) ad (7, 280)

a)What is the half life of this decay process?
b)What is the initial value of the quantity being measured?

thanks alot

Use the model $m = m_0 e^{-kt}$.

Substitute (3, 560) and (7, 280) into the model to get two equations in $\, m_0 \,$ and $\, k \,$.

Solve these equations simultaneously, get the values of $\, m_0 \,$ and $\, k \,$ and substitute their values into the model.

a) Substitute $m = \frac{m_0}{2}$ into the model and solve for t.

b) $\, m_0 \,$.
• Feb 15th 2008, 07:16 PM
icetea
thanks

but im not sure how to sub in the points into the model like how for example the point (3,560)

could you sub in one of the points for me?
• Feb 15th 2008, 07:48 PM
mr fantastic
Quote:

Originally Posted by icetea
thanks

but im not sure how to sub in the points into the model like how for example the point (3,560)

could you sub in one of the points for me?

$m = m_0 e^{-kt}$:

(3, 560): $3 = m_0 e^{-560k}$ .... (1)

(7, 280): $7 = m_0 e^{-280k}$ .... (2)

(2)/(1): $\displaystyle \frac{7}{3} = \frac{e^{-280}}{e^{-560k}} = e^{280k} \Rightarrow \ln \frac{7}{3} = 280k \Rightarrow k = \frac{1}{280} \ln \frac{7}{3} \approx .....$ (I suggest finding k correct to at least 4 decimal places).

Now sub your value of k into either of (1) or (2) and solve for $m_0$ .....