# half life solving initial quantity

• March 23rd 2008, 07:12 PM
theman
half life solving initial quantity
half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

I need to solve for the initial quantity with the info given, thx for the help
• March 23rd 2008, 07:16 PM
Jhevon
Quote:

Originally Posted by theman
half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

I need to solve for the initial quantity with the info given, thx for the help

we use the equation $I(t) = I_0e^{rt}$

where $r$ is the rate of decay, $I(t)$ is the amount at time $t$, $I_0$ is the intial amount (what we are searching for).

now, $\mbox{half-life} = \frac {\ln 2}r$

you know the half-life, so you can find $r$.

once you have $r$. plug in $I(t) = 1.5$, $t = 1000$, and $r =$ whatever. and solve for $I_0$
• March 23rd 2008, 07:25 PM
theman
thanks, but i still dun know how to solve for the rate of the decay...
• March 23rd 2008, 07:40 PM
topsquark
Quote:

Originally Posted by Jhevon
now, $\mbox{half-life} = \frac {\ln 2}r$

you know the half-life, so you can find $r$.

Quote:

Originally Posted by theman
thanks, but i still dun know how to solve for the rate of the decay...

You can't solve that equation for r??

-Dan
• March 23rd 2008, 07:55 PM
theman
lol, sorry, im kinda stupid, but i just solved it thanks!
• March 23rd 2008, 07:56 PM
theman
um, sorry, but one more thing. With the same info and the initial quantity i got was 2.3 g. How would u solve it for 10,000 years.
• March 23rd 2008, 07:59 PM
topsquark
Quote:

Originally Posted by theman
um, sorry, but one more thing. With the same info and the initial quantity i got was 2.3 g. How would u solve it for 10,000 years.

$I = I_0 e^{rt}$

You have $I_0$ and r. Just plug in t = 10000 years.

-Dan
• March 23rd 2008, 08:10 PM
mr fantastic
Quote:

Originally Posted by theman
half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

I need to solve for the initial quantity with the info given, thx for the help