# modelling!

• Jun 29th 2013, 08:48 AM
lawochekel
modelling!
A radio active element is know to decay at the rate of 2% every 20yrs. If initially you add 165g of the element, how much would you have in 60yrs.
what is the half life time of the element.

i formulated the model as

\$\displaystyle E_{t+1} = 1.02E_{t} , where t \sim O(20) \$

\$\displaystyle E_{0} = 165g \$

\$\displaystyle t= 0 \$

solution

\$\displaystyle E_{1} = 1.02E_{0} \$

\$\displaystyle t= 3 \$

\$\displaystyle E_{4} = 1.02^4 E_{0} = 1.02^4 * 165 (in 60yrs) \$

pls cross check to correct me and how do i compute the half life?

thanks
• Jun 29th 2013, 09:14 AM
topsquark
Re: modelling!
The half-life equation is exponential and continuous so a discrete model isn't going to work here. Read this.

Now, a 1/2 life is the time it takes for 50% of the material to decay. You know that 2% of your material decays in 20 years. So how much time would it take for 50% to go?

-Dan
• Jun 29th 2013, 09:39 AM
Shakarri
Re: modelling!
In your answer where you have 1.02 it should be 1/1.02 and in the last line the index should be 3 not 4.
After n half lives the original mass