SOLUTION: Strontium–90 has a half-life of 29 years. How long will it take for an initial sample of 10 mg to decay to 1 mg? Do I use the formula A= Ao(1/2)^t/h If yes I come up with 1=10(

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Strontium–90 has a half-life of 29 years. How long will it take for an initial sample of 10 mg to decay to 1 mg? Do I use the formula A= Ao(1/2)^t/h If yes I come up with 1=10(      Log On


   



Question 260017: Strontium–90 has a half-life of 29 years. How long will it take for an initial sample of 10 mg to decay to 1 mg?
Do I use the formula A= Ao(1/2)^t/h
If yes I come up with 1=10(1/2)^t/29 which ends up to be wrong.
So how do I proceed? Please HELP!!!

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Strontium–90 has a half-life of 29 years. How long will it take for an initial sample of 10 mg to decay to 1 mg?
.
You can apply the general "exponential decay" modeled by:
A+=+Ie%5E%28kt%29
Where
A is the final amount
I is the initial amount
k is a constant
t is time
.
A+=+Ie%5E%28kt%29
Plugging in your given information to first find k:
%281%2F2%2910+=+10e%5E%28k%2A29%29
5+=+10e%5E%28k%2A29%29
1%2F2+=+e%5E%28k%2A29%29
ln%281%2F2%29+=+29k
ln%281%2F2%29%2F29+=+k
-.0239016+=+k
.
Now, your actual model is:
A+=+Ie%5E%28-.0239016t%29
.
And we can use to to answer your question.
How long will it take for an initial sample of 10 mg to decay to 1 mg?
A+=+Ie%5E%28-.0239016t%29
1+=+10e%5E%28-.0239016t%29
.1+=+e%5E%28-.0239016t%29
ln%28.1%29+=+-.0239016t
ln%28.1%29%2F-.0239016+=+t
96.34 yrs = t