SOLUTION: 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 microorgani
Question 1192769: 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? Answer by ikleyn(52778) (Show Source):
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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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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
= -17.5217, = 17.1217.
According to the meaning of the problem, you ignore the negative root and accept the positive one.
Your ANSWER is the value x= 17.1217 hours.
