Question 1187783
.
Find the half-life of a certain radioactive substance which decays according to the formula 𝑦 = {{{100*e^(-3t)}}}, 
where y is the amount present after t years?
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<pre>
The initial mass is 100 units at t= 0.


At the half-life value of t,  the remaining mass is  {{{100/2}}} = 50.


So we write the decay equation in  ekt-form


    50 = {{{100*e^(-3t)}}}

    {{{50/100}}} = {{{e^(-3t)}}}

    0.5 = {{{e^(-3t)}}}


Take logarithm base "e"  (natural logarithm) of both sides


   ln(0.5) = -3t


Express "t" and calculate


    t = {{{ln(0.5)/(-3)}}} = 0.231049  years.    <U>ANSWER</U>


<U>CHECK</U>.  {{{100*e^(-3*0.231049)}}} = {{{100*2.71828^(-3*0.231049)}}} = use your calculator = 50.0000    ! precisely correct !
</pre>

Solved.


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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.



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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>".



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