Question 1189594
.
The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. 
The doubling time for this substance was observed to be 23 days. 
There were 72.6 mg of the substance present at the beginning of the study.
(a) Let t be the time (in days) since the beginning of the study, and let
y be the amount of the substance at time t. Write a formula relating y to t. 
Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
(b) How much will be present in 8 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
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            This problem can be solved in couple of lines with very short simple calculations.


            See my solution below.



<pre>
As the mass is doubling every 23 days, we can write

    y = 72.6*2^(t/23),      (1)

where t is the time in days.  It is LITERAL TRANSLATION of what the problem states.


Formula (1) is the answer to question (a).


To answer question (b), simply substitute t= 8 days into the formula and calculate 

    y = 72.6*2^(8/23) = use your calculator = 92.39377 milligrams (rounded).
</pre>

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That is all. &nbsp;&nbsp;The problem is just solved in full.


It is easy and a &nbsp;&nbsp;<U>S T A N D A R D</U> &nbsp;&nbsp;way to solve exponential growth problems, 
when the doubling period is given as an input data.



May god save you from making tons unnecessary and nonsensical calculations, &nbsp;which @Theo does in his post.


For peace in your mind, &nbsp;simply ignore his post. &nbsp;It is definitely wrong way to teach.



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To see many similar and different solved problems of this kind, &nbsp;look into the lessons

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in this site.


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.