SOLUTION: The number of fruit flies F(x) in a farming area depends on the spring rainfall x: F(x) = 15x – x^2. What rainfall produces the maximum number of fruit flies? A. 225 in. B.

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Question 440163: The number of fruit flies F(x) in a farming area depends on the spring rainfall x: F(x) = 15x – x^2. What rainfall produces the maximum number of fruit flies?
A. 225 in.
B. 0 in.
C. 7.5 in.
D. 15 in.


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

The number of fruit flies F(x) in a farming area depends on the spring rainfall x: 

 f(x) = -x^2+15x  |graphically a parabola opening downward a< 0

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

 f(x) = -(x -7.5)^2 + 56.25     | completing the square to find the vertex

 Vertex is Pt(7.5, 56.25)

     7.5" rainfall produces the maximum number of fruit flies