Question 1201552
.
The radioactive isotope of potassium-42, which is vital in the diagnosis of brain tumors, 
has a half-life of 12.36 hours.
If 500-mg of potasium-42 was taken, how many milligrams of this isotope will remain after 48 hours?
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<pre>
Since you are given the half-life time period of 12.36 hours,
use the standard exponential decay formula with the base (1/2)

    m(t) = {{{m(0)*(1/2)^(t/12.36)}}},


where m(0) is the starting mass at t= 0  and  m(t) is remaining mass in the current time moment t,  
t is the time in hours.


To answer the problem's question, calculate the remaining mass at t = 48 hours using the formula

    m(t) = {{{500*(1/2)^(48/12.36)}}} = 33.8783 grams (rounded).    <U>ANSWER</U>
</pre>

Solved, answered and explained.


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On radioactive decay, &nbsp;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.


You will find many similar &nbsp;(and different) &nbsp;solved problems there.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Use this lesson as your handbook, &nbsp;textbook, &nbsp;guide, &nbsp;tutorials, and &nbsp;(free of charge) &nbsp;home teacher.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Learn the subject from there once and for all.



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The major reason, &nbsp;why I started write this my post, &nbsp;is to teach you that in radio-active decay problems,
when the half-life is given, &nbsp;you should use the exponential decay model with the base &nbsp;1/2,
which leads you to the end and to the answer by a &nbsp;SHORTEST &nbsp;way.


It is not only the &nbsp;SHORTEST way in such problems, &nbsp;but it is the &nbsp;EXPECTED &nbsp;way, &nbsp;too.


Finally, &nbsp;it is not only the shortest way and not only the expected way: 

it is a &nbsp;GOOD &nbsp;STYLE &nbsp;way, &nbsp;which demonstrates 

that you do understand the subject in full and &nbsp;PRECISELY &nbsp;as it is.