Question 1198803
.


How @Theo solves this problem,  is  WRONG  TEACHING.



The standard method for this formulation is shown in the post by @math_tutor2020.



It is short, straightforward and  EXCLUDES  100  tons of unnecessary calculations
that @Theo makes in his post.


<pre>
    +-------------------------------------------------------------------------+
    |           When the problem gives the-half life duration,                |
    |         the correct analytic solution of  a  decay problem              |
    |    MUST be started from writing exponential decay function base 1/2,    |
    | if the opposite is not requested by the problem directly and explicitly.|
    |                                                                         |
    |    So called "ekt-form" is IRRELEVANT in such cases, so avoid use it,   |
    |             if you do not want to appear incompetent.                   |
    +-------------------------------------------------------------------------+
</pre>

See also my lesson on radioactive decay problems under the link

&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.



This problem should be and must be solved in &nbsp;5 - 6 - 7 &nbsp;lines, &nbsp;no more than that.