Final answer:
Using the two given points during the flu season, we calculate the slope of the reduction in patients per week and use one of the points to find the y-intercept. The resulting linear equation representing the number of patients seen each week at the clinic is f(x) = -5x + 100, which corresponds to option B.
Step-by-step explanation:
To find the function that represents the number of patients seen each week during flu season at a medical clinic, we can use the two data points provided: In week 5, there were 75 patients (point 1: (5, 75)), and in week 10, there were 50 patients (point 2: (10, 50)). The goal is to find a linear equation of the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.
First, we find the slope (m) using the formula:
m = (Y2 - Y1) / (X2 - X1)
Substituting the given values, we get:
m = (50 - 75) / (10 - 5) = -25 / 5 = -5
Now we use one of the points to find the y-intercept (b).
Using point (5, 75):
75 = (-5)(5) + b
75 = -25 + b
b = 75 + 25
b = 100
So the equation of this function in function form is:
f(x) = -5x + 100
Therefore, the correct option is B. f(x) = -5x + 100.