The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by m(x)=-x(x-4) What amount of rainfall results in the maximum number of mosquitoes? centimeters

Question

The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by  m(x)=-x(x-4) What amount of rainfall results in the maximum number of mosquitoes? centimeters

Bytelearn · Accepted Answer

Identify Quadratic Function: To find the amount of rainfall that results in the maximum number of mosquitoes, we need to analyze the given quadratic function m(x) = -x(x - 4), which is a parabola that opens downwards (since the coefficient of x^2 is negative). The maximum value of this function occurs at its vertex.Find Vertex Formula: The vertex of a parabola in the form of f(x) = ax^2 + bx + c can be found using the formula x = -b/(2a). In our case, the function m(x) = -x(x - 4) can be rewritten as m(x) = -x^2 + 4x. Here, a = -1 and b = 4.Calculate Vertex: Using the vertex formula x = -b/(2a), we substitute a = -1 and b = 4 to find the x-coordinate of the vertex, which will give us the amount of rainfall that maximizes the number of mosquitoes. So, x = -4/(2*(-1)) = -4/(-2) = 2.Determine Maximum Rainfall: The x-coordinate of the vertex is 2 centimeters. This means that 2 centimeters of rainfall results in the maximum number of mosquitoes according to the model m(x) = -x(x - 4).

The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by $\newline$ $m(x)=-x(x-4)$ $\newline$ What amount of rainfall results in the maximum number of mosquitoes? $\newline$ $\text{centimeters}$

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The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by\newlinem(x)=−x(x−4)m(x)=-x(x-4)m(x)=−x(x−4)\newlineWhat amount of rainfall results in the maximum number of mosquitoes?\newlinecentimeters\text{centimeters}centimeters

The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by $\newline$ $m(x)=-x(x-4)$ $\newline$ What amount of rainfall results in the maximum number of mosquitoes? $\newline$ $\text{centimeters}$