Question

What is the maximum possible number of mosquitoes, given the function m(x) = -x(x - 4) modeling the relationship between rainfall (x) and the number of mosquitoes in Brooklyn (in millions)?

Answer 1

The maximum possible number of mosquitoes, as represented by the given function, is -4 million mosquitoes.

Step-by-step explanation:

The given function is m(x) = -x(x - 4) representing the relationship between rainfall (x) and the number of mosquitoes in Brooklyn (in millions). In order to find the maximum possible number of mosquitoes, we need to determine the vertex of the parabola represented by the function.

The vertex of a parabola with the equation y = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)). In this case, a = -1 and b = 4. Plugging these values into the vertex formula, we get:

x = -4 / (2(-1)) = 2

Substituting this value of x back into the function, we can find the maximum number of mosquitoes:

m(2) = -(2)(2 - 4) = -4

Therefore, the maximum possible number of mosquitoes, as represented by the function, is -4 million mosquitoes.

Answer 2

The maximum possible number of mosquitoes is 4 million mosquitoes.

Step-by-step explanation:

The maximum possible number of mosquitoes can be determined by finding the maximum value of the function m(x) = -x(x - 4). To find the maximum, we can use the vertex formula for a quadratic function, which is x = -b/2a. For this function, a = -1 and b = 4. Plugging these values into the formula, we get x = -4/2(-1) = 2. Therefore, the maximum number of mosquitoes occurs when x = 2.

Substituting x = 2 into the function, we get m(2) = -2(2 - 4) = -2(-2) = 4. So, the maximum possible number of mosquitoes is 4 million mosquitoes.