Question 1162420
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<pre>

We are given that the half-life period is 78 years;  therefore, we can write


    p(t) = {{{(1/2)^(t/78)}}},      (1)


where p(t) is the remaining mass fraction. (It is the standard radioactive decay model in terms of half-life period).


The problem asks to determine the time "t" when p(t) = 0.6.


In this case, the equation (1) takes the form


    0.6 = {{{(1/2)^(t/78)}}}.


Take logarithm base 2 of both sides


    {{{log(2,(0.6)))}}} = {{{(t/78)*log(2, (1/2))}}}


    t = {{{(78*log(2,(0.6)))/((-1))}}} = {{{(-78)*log(2,(0.6))}}} = 57.48 years.    <U>ANSWER</U>
</pre>

Solved.


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See 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 and find there many other similar solved problems.


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 lessons are 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.



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The lesson to learn from my post is THIS:


<pre>
    If you are given input data in terms of half-life, you do not need to convert your data 

    into ekt-model.  Such conversion is an excessive work and unnecessary calculations.


    You can complete all calculations in terms of the half-life model, working consistently with degrees of 2, 
    which is your base in this case..
</pre>