Solve.
-The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$, in millions, in a certain area depends on the June rainfall $x$, in inches, according to the function $\mathrm { M } ( \mathrm { x } ) = 3 \mathrm { x } - \mathrm { x } ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?
A) $1.5 \mathrm { in }$.
B) $9 \mathrm { in }$.
C) $0 \mathrm { in }$.
D) 3 in.

Question

Quizplus · Accepted Answer

To find the maximum number of mosquitoes, we need to find the vertex of the parabola represented by the function $M(x) = 3x - x^2$. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$, where $a = -1$ and $b = 3$. Thus, $-\frac{3}{2(-1)} = 1.5$, indicating that the maximum number of mosquitoes occurs with 1.5 inches of rainfall.

Solve -The Number of Mosquitoes M(x)\mathrm { M } ( \mathrm { x } )M(x)

Solve
-The Number of Mosquitoes $\mathrm { M } ( \mathrm { x } )$