Question

The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:
m(x)=-x^2+14x

What is the maximum possible number of mosquitoes?

Answer 1

Answer:

49 million

Step-by-step explanation:

The equation is:

$m(x)=-x^2+14x$

Which is a quadratic function of the form  $y=ax^2+bx+c$

So, matching the equation with general form of quadratic function, we see:

a = -1

b = 14

c = 0

The x is the independent variable (rainfall in cm) and the function is dependent on the rainfall amount, as the number of millions of mosquitoes.

The max of the function occurs at the value  $x=-\frac{b}{2a}$

Lets substitute and find:

$x=-\frac{b}{2a}=-\frac{14}{2(-1)}=7$

So, max occurs at x = 7, if we find the function value at x = 7, we get the max amount of mosquitoes. Shown below:

$m(x)=-x^2+14x\\m(7)=-7^2+14(7)\\m(7)=49$

According to the equation, the max number of mosquitoes is 49 million

Answer 2

Answer:

49 million mosquito's

Step-by-step explanation:

Hope this helps!