SOLUTION: The half-life of {{{Pu^230}}} is 1620 years. If 2.1 grams remian after 1000 years, whay is the initial quantity anf how much will remain after 10000 years? I am using the {{{A=P

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Question 289652: The half-life of Pu%5E230 is 1620 years. If 2.1 grams remian after 1000 years, whay is the initial quantity anf how much will remain after 10000 years?
I am using the A=Pe%5Ert formula and so far have 2.1=Pe%5E%2824360+X+1000%29, have I set this up right? If so, where do I go from here?
Thanks for your help!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The half-life of Pu 230 is 1620 years.
If 2.1 grams remain after 1000 years, what is the initial quantity?
:
The half life equation is: A = Ao*2^(-t/h)
where
A = the resulting amt after t years
Ao = initial amt (t=0)
t = time in yrs
h = half-life of the substance
:
Find the initial qty
Ao*2^(-1000/1620) = 2.1
Ao*2^-.617284
Using a calc: enter 2^-.617284 and you have:
.6519Ao = 2.1
Ao = 2.1%2F.6519
Ao = 3.22 grams is the initial qty
:
Check on a calc: enter 3.22*2^(-1000/1620) = 2.099 ~ 2.1, confirms our solution
:
:
how much will remain after 10000 years?
Using Ao = 3.22, find A
A = 3.22*2^(-10000/1620)
using a calc
A = .044 grams after 10,000 years