SOLUTION: The half life of thorium-229 is 7340 yrs. how long will it take a sampleof this substance to decay to 20% of its original amount? That is the problem. I need help finding the so

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Question 395072: The half life of thorium-229 is 7340 yrs. how long will it take a sampleof this substance to decay to 20% of its original amount?
That is the problem. I need help finding the solution. I know I will use the model A=Aoe^kt. I believe it would go something like:
A/2=Ao/2 ^kt
0.2=???
I need to find my K before I can go further, but I am not sure how to do that. I would appreciate any help! Thank you!!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The half life of thorium-229 is 7340 yrs.
how long will it take a sampleof this substance to decay to 20% of its original amount?
:
I think the equation should be:
A = Ao*2^(-t/h)
where
A = amt after t yrs
Ao = initial amt
t = time in yrs
h = half-life of the substance
:
Using the initial amt, Ao = 1, then A = .2
2^(-t/7340) = .2
Using natural logs
*ln(2) = ln(.2)
=
= -2.3219281
t = -7340 * -2.3219281
t = 17,043 yrs
:
:
Check solution on calc:
enter 2^(-17043/7340), result: .19999 ~ .2, confirms our solution of t = 17,043 yrs