Question 1187575
.
A radioactive form of uranium has a half life of 2.5x 10^5 years. 
a) Find the remaining mass of 1 g sample after t years
b) Determine the remaining mass of this sample after 5000 years.
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            In his post, @Theo makes tons of absolutely unnecessary work,  unnecessary calculations 

            and unnecessary explanations,  making simple problem hopelessly confused and showing you  WRONG  WAY  doing job.


            Had some student come to his teacher and present a solution like @Theo does in his post,

            the teacher would only shrug shoulders  (out of curtesy).


            I came with two goals:   1)   to make the solution in a regular/normal simple manner,  and 

                       &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2) &nbsp;&nbsp;to make the solution in a way &nbsp;<U>HOW &nbsp;TO &nbsp;&nbsp;it should be done and presented</U>.



<pre>
Since the half life is given, we write the decay equation using the " base 2 " exponent function


    m(t) = {{{m(0)*(1/2)^(t/250000)}}}


for a current mass m(t),  where m(0) is the initial mass of the sample.


Now we simply substitute the given values into the formula and calculate


(a)  1 gram sample after t years  m(t) = {{{(1/2)^(t/250000)}}}  grams.


(b)  the remaining mass of this sample after 5000 years is  m(5000) = {{{(1/2)^(5000/250000)}}} = {{{(1/2)^(1/50)}}} = {{{(1/2)^0.02}}} = 0.9862327.    <U>ANSWER</U>
</pre>

That is all.  &nbsp;&nbsp;&nbsp;&nbsp;The problem is just solved and completed.



What you need to know to solve such problems, &nbsp;is &nbsp;THIS:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- there are different forms of exponential decay equations: &nbsp;1) &nbsp;ekt-form; &nbsp;2) &nbsp;" base 2 " &nbsp;form; &nbsp;and &nbsp;3) &nbsp;an arbitrary &nbsp;" base &nbsp;b " form.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- each form is good for its own purposes and problems;


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- if the problem's data is given in half-life terms, &nbsp;always use &nbsp;" base 2 " &nbsp;form and make all calculations in this form;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do not change this form in the course of the solution, &nbsp;until the problem asks you to change the base explicitly.



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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.



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

Learn the subject from there once and for all.



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