Question 1176085
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The half-life of cobalt - 60 is 5.27 years. Starting with a sample of 150 mg, after how many years is 20 mg left?
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<pre>
Since the half-line is given in the problem, you can write the decay formula in this form

    M = {{{M[0]*(1/2)^(t/5.27)}}}.


In this equation,  {{{M[0]}}}  is the starting mass of the radioactive material;  

M is the current mass after t yeras of decay.



In the problem, you are given  {{{M[0]}}} = 150 mg  and  M = 20 mg, and they want you find t.


So, your equation is

    20 = {{{150*(1/2)^(t/5.27)}}}.


Divide both sides by 150

    {{{20/150}}} = {{{(1/2)^(t/5.27)}}},   or   0.1333 = {{{(1/2)^(t/5.27)}}}.


Take logarithm base 10 of both sides

    log(0.1333) = {{{(t/5.27)*log((0.5))}}}


and express t from the last equation

    t = {{{(5.27*log((0.1333)))/log((0.5))}}}.


Now use your calculator

    t = 15.32 years.     <U>ANSWER</U>
</pre>

Solved.


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To learn more on the subject, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Radioactive-decay-problems.lesson>Radioactive decay problems</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Logarithms</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.