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? 
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You can apply the general "exponential decay" modeled by:
{{{A = Ie^(kt)}}}
Where
A is the final amount
I is the initial amount
k is a constant
t is time
.
{{{A = Ie^(kt)}}}
Plugging in your given information to first find k:
{{{(1/2)10 = 10e^(k*29)}}}
{{{5 = 10e^(k*29)}}}
{{{1/2 = e^(k*29)}}}
{{{ln(1/2) = 29k}}}
{{{ln(1/2)/29 = k}}}
{{{-.0239016 = k}}}
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Now, your actual model is:
{{{A = Ie^(-.0239016t)}}}
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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^(-.0239016t)}}}
{{{1 = 10e^(-.0239016t)}}}
{{{.1 = e^(-.0239016t)}}}
{{{ln(.1) = -.0239016t}}}
{{{ln(.1)/-.0239016 = t}}}
96.34 yrs = t