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

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- Mar 23rd 2008, 06:12 PMthemanhalf 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 - Mar 23rd 2008, 06:16 PMJhevon
we use the equation $\displaystyle I(t) = I_0e^{rt}$

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

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

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

once you have $\displaystyle r$. plug in $\displaystyle I(t) = 1.5$, $\displaystyle t = 1000$, and $\displaystyle r = $ whatever. and solve for $\displaystyle I_0$ - Mar 23rd 2008, 06:25 PMtheman
thanks, but i still dun know how to solve for the rate of the decay...

- Mar 23rd 2008, 06:40 PMtopsquark
- Mar 23rd 2008, 06:55 PMtheman
lol, sorry, im kinda stupid, but i just solved it thanks!

- Mar 23rd 2008, 06:56 PMtheman
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.

- Mar 23rd 2008, 06:59 PMtopsquark
- Mar 23rd 2008, 07:10 PMmr fantastic
(Swear) double posts (Headbang) .