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 is the maximum possible number of mosquitoes? million mosquitoes

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 is the maximum possible number of mosquitoes? million mosquitoes

Bytelearn · Accepted Answer

Identify function type: Identify the type of function. The function m(x) = -x(x - 4) is a quadratic function in the form of m(x) = ax^2 + bx + c, where a = -1, b = 4, and c = 0.Determine axis of symmetry: Determine the axis of symmetry for the quadratic function. The axis of symmetry for a quadratic function in the form of m(x) = ax^2 + bx + c is given by the formula x = -b/(2a). For our function, a = -1 and b = 4. x = -4/(2 * -1) = -4/(-2) = 2Calculate maximum value: Calculate the maximum value of the function. The maximum value of the function occurs at the axis of symmetry. To find the maximum number of mosquitoes, we substitute x = 2 into the function m(x). m(2) = -2(2 - 4) = -2(-2) = 4Interpret the result: Interpret the result. The maximum possible number of mosquitoes is 4 million when the rainfall is 2 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 is the maximum possible number of mosquitoes? $\newline$ million mosquitoes

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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 is the maximum possible number of mosquitoes?\newlinemillion mosquitoes

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 is the maximum possible number of mosquitoes? $\newline$ million mosquitoes