Question

The function ggg models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area.

Answer 1

Answer:

6cm produces the largest mosquito

Step-by-step explanation:

The question has missing details.

From the complete question, the function is:

$g(x) = 12x-x^2$

Required

Which area of rainfall produces the most mosquito

This implies that, we calculate the maximum of the function.

This is calculated as:

$Max = -\frac{b}{2a}$

We have:

$g(x) = 12x-x^2$

Rewrite as:

$g(x) = -x^2 + 12x + 0$

From the above:

$a= -1$

$b = 12$

$c = 0$

So, we have:

$Max = -\frac{b}{2a}$

$Max = -\frac{12}{2 * -1}$

$Max = \frac{12}{2}$

$Max = 6$

This implies that:

$x = 6$ ---- the maximum

When rainfall is at 6cm, there is a maximum number of mosquitoes

The maximum is then calculated as:

$g(x) = 12x-x^2$

$g(6) = 12 * 6 - 6^2$

$g(6) = 72 - 36$

$g(6) = 36$

The maximum number of mosquito is 36 million