exponential decay model

[pgotm]

:shock:
I have a problem and i fgured out the formula but not where to put what where.
Question: Find the intial quanity in grams of the iostope Ra^226 if the half life is 1620 years and the amount after 1000 years is .15 grams.
1/2a=Ae ^k(162)
1/2=e^1620k
ln (.5) = ln (e^1620k)
ln (.5)=1620k
k=ln.5 over 1620
R=Ae^-0.000427869t
I'm not sure where to put everything in because my answers come out so wrong. THanks for any help

 

[skeeter]

A = A₀e^kt

A₀/2 = A₀e^1620k

1/2 = e^1620k

ln(1/2) = 1620k

k = [ln(1/2)]/1620 = approx -4.278686...

.15 = A₀e^1000k

A₀ = .15/[e^1000k] = .23 grams