Question 1179797
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<pre>

An exponential model has the form


    N(t) = {{{a*b^t}}}, 


where "a" is the initial number of bacteria, "b" is the base of the exponential function and t is the time in hours.


In our case,  the initial value is  a = 800; so we can write this equation


    1280 = {{{800*b^2}}},


describing the scene in 2 hours.


From this equation,


    b = {{{sqrt(1280/800)}}} = {{{sqrt(1.6)}}} = 1.264911.


So, your exponential function is


    N(t) = {{{800*1.264911^t}}}.     <U>ANSWER</U>


First question is answered.


To answer the second question, substitute t = 48 hours ("2 days") into the formula


    N(24) = {{{800*1.264911^48}}} = 63382376.      <U>ANSWER</U>
</pre>

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The problem is fully solved.



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To see many similar &nbsp;(and different) &nbsp;solved problems on bacteria growth, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Bacteria-growth-problems.lesson>Bacteria growth problems</A> 

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 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.