Q:

A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season, the clinic saw 90 patients. In week 10 of flu season, the clinic saw 60 patients. Assume the reduction in the number of patients each week is linear. Write an equation in function form to show the number of patients seen each week at the clinic.

Accepted Solution

A:
Answer:[tex]f(x) = -6x +120[/tex]Step-by-step explanation:Let's call y the number of patients treated each weekLet's call x the week number.If the reduction in the number of patients each week is linear then the equation that models this situation will have the following form:[tex]y = mx + b[/tex]Where m is the slope of the equation and b is the intercept with the x-axis.If we know two points on the line then we can find the values of m and b.We know that During week 5 of flu season, the clinic saw 90 patients, then we have the point:(5, 90)We know that In week 10 of flu season, the clinic saw 60 patients, then we have the point:(10, 60).Then we can find m and b using the followings formulas:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] Β  and [tex]b=y_1-mx_1[/tex]In this case: [tex](x_1, y_1) = (5, 90)[/tex] and [tex](x_2, y_2) = (10, 60)[/tex]Then:[tex]m=\frac{60-90}{10-5}[/tex][tex]m=-6[/tex]And [tex]b=90-(-6)(5)[/tex][tex]b=120[/tex]Finally the function that shows the number of patients seen each week at the clinic is:[tex]f(x) = -6x +120[/tex]