Question 1192769
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A population of microorganisms grows according to the function p(x) = 100+0.2x+0.5x^2, 
where x is given in hours. How many hours does it take to reach population of 250 microorganisms?
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<pre>
To answer the question, you should solve this quadratic equation

    100 + 0.2x + 0.5x^2 = 250.


Reduce the equation to the standard form quadratic equation

    0.5x^2 + 0.2x - 150 = 0


and apply the quadratic formula.  You will get the roots

    {{{x[1]}}} = -17.5217,   {{{x[2]}}} = 17.1217.


According to the meaning of the problem, you ignore the negative root and accept the positive one.


Your <U>ANSWER</U> is the value  x= 17.1217 hours.
</pre>

Solved.


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On solving quadratic equations using the quadratic formula, &nbsp;see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

in this site.