Maximum Number of Mosquitoes The number of mosquitoes Mx in

Maximum Number of Mosquitoes The number of mosquitoes. M(x). in millions, in a certain area of Florida depends on the June rainfall, x, in inches. The function M(x) = 10x-x^2 models this phenomenon. Find the amount of rainfall that will maximize the number of mosquitoes. What is the maximum number of mosquitoes?

Solution

M(x) = 10x -x^2 where x is rainfall in inches and M(x) is mosquitos in millions

Now M(x) is a quadratic equation of form y = ax^2 +bx +c

Its maximum valueslies on vertex i.e. x = -b/2a and y(-b/2a)

Now x =-b/2a = -10/(-2) =5 inches rainfall would cause maximum no. of mosquitos

M(5) = 10*5 - 5^2 = 50 -25 = 25 millions mosquitos