SOLUTION: The number of Americans with a particular disease can be approximately by f(x) = -727x^2 + 10300x - 939, where x is the number of years since 1986. Based on the model, what was the

Question 1051387: The number of Americans with a particular disease can be approximately by f(x) = -727x^2 + 10300x - 939, where x is the number of years since 1986. Based on the model, what was the largest number of people with this disease?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) f(x) = -727x^2 + 10300x - 939
:
We take the first derivative of this equation (it is a parabola that curves downward) and set it equal to zero, then solve for x - this will give us the x coordinate of the vertex)
:
-1454x + 10300 = 0
:
-1454x = -10300
:
x = 7.0839
:
We substitute for x in equation 1) to get the y coordinate of the vertex - this is the largest number of people with this disease
:
y = -727(7.0839)^2 + 10300(7.0839) - 939 = 35543.1183
:
*******************************************************
rounding y to the nearest whole person
:
The largest number of people with this disease is 35,543
*******************************************************
:

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