Question

A medical is reducing the number of incoming patients are giving vaccines before flu season during week 5 of Lucy's in the clinic saw 85 patients in a week 10 of flu season the clinic saw 65 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 A:f(x)=20x+85B:f(x)=-20x+85C: f(x)=4x+105D:f(x)=-4x+106

Answer 1

number of patients at the given weeks:

week 5: 85 patients

week 10: 65 patients

We need to select a function from the options that, for a given week "x" we get an approximate to the number of patients that they had in those weeks.

One consideration is that the number of patients is decreasing:

week 5 is 85

and week 10 is 65.

What that means is that the function we choose, should have a negative number that accompanies the variable "x" to represent this decrese in patients.

Our two valid options are:

`\begin{gathered} B\colon f\mleft(x\mright)=-20x+85 \\ D\colon f\mleft(x\mright)=-4x+106​ \end{gathered}`

First we try option B. For 5 weeks x =5, and we get:

`\begin{gathered} f(5)=-20(5)+85 \\ f(5)=-100+85 \\ f(5)=-15 \end{gathered}`

And since -15 is not even close to the number of patients on week 5, We discard this option.

Now we try option D, for week 5 (x=5), we get:

`\begin{gathered} f(5)=-4(5)+106 \\ f(5)=-20+106 \\ f(5)=86 \end{gathered}`

Which is really close to the number of patients on week 5.

We corroborate for week 10, x=10:

`\begin{gathered} f(10)=-4(10)+106 \\ f(10)=-40+106 \\ f(10)=66 \end{gathered}`

Which is also really close to the value for week 10.

Thus, our answer is:

`D\colon f\mleft(x\mright)=-4x+106​`