Question 168549: the number of mosquitoes M(x)in millions, in a certain area depends on the june rainfall x, in inches, according to the function M(x) =12x-x^2 What rainfall produces the maximum number of mosquitoes
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! looks like m(x) = 12x - x^2 is a quadratic equation which is equivalent to:
m(x) = -x^2 + 12x + 0
since this is a quadratic, the max/min point is given by the formula -b/2a.
standard form of quadratic is:
ax^2 + bx + c
in your equation, b = 12, and a = -1.
-b/2a = -12/-2 = 6.
max/min point should be when x = 6.
since the coefficient of x^2 (represented by a in the standard form) is minus, this graph has it's head pointing upwards and it's tails pointing downwards, so x = 6 leads to a maximum point.
when x = 6, the equation becomes:
-x^2 + 12x + 0 = -(6)^2 + 12(6) = -36 + 72 = 36.
the maximum point on the graph is (6,36).
what this says is that m(6) = 36 which means when the rainfall is 6 inches in june, 36 million mosquitoes are produced, and that is the maximum number of mosquitoes that will be produced in that area.
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graph of this equation shows up as follows:
x axis is in inches.
y axis is in millions of mosquitors.
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