Question

The number of gnats G(x), in millions, in a certain area depends on the May rainfall x, in inches. That relationship can be expressed by the quadratic function G(x) = - x2 + 18x How many inches of rainfall produces the maximum number of gnats?

Answer 1

Answer:

9 inches of rainfall produces the maximum number of gnats.

Step-by-step explanation:

Given : $G(x) = - x^2 + 18x$

To Find :How many inches of rainfall produces the maximum number of gnats?

Solution:

$G(x) = - x^2 + 18x$

G(x) =The number of gnats in millions.

x denotes the length of rainfall

To Find the maximum length find the mid point of zeroes .Since parabolas are symmetrical, the x value of the max falls 1/2 way between the zeros.

$0= - x^2 + 18x$

$0= x^2-18x$

$0= x(x-18)$

So, x = 0 , x= 18

Now Formula of midpoint : $x=\frac{x_1+x_2}{2}$

$x=\frac{0+18}{2}$

$x=9$

Hence 9 inches of rainfall produces the maximum number of gnats.