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

We start with the given function for the number of mosquitoes (in millions):   m(x) = –x(x – 4) First, expand the function:   m(x) = –x² + 4x This is a quadratic function that opens downward (since the coefficient of x² is negative), which means it has a maximum value at its vertex. The x-coordinate of the vertex for a quadratic function ax² + bx + c is given by:   x = –b / (2a) Here, a = –1 and b = 4. Plugging in these values:   x = –4 / (2 × –1) = 2 Now, substitute x = 2 into the function to find the maximum number of mosquitoes:   m(2) = –(2)² + 4(2) = –4 + 8 = 4 Since m(x) is given in millions of mosquitoes, the maximum possible number of mosquitoes is 4 million. Thus, the answer is: 4 million mosquitoes.