Answer:
[tex]s(p) =\frac{77p}{1075}[/tex]
Step-by-step explanation:
Given
s = sales tax
p = retail price
The variation is represented as:
[tex]s\ \alpha\ p[/tex]
s = 12.32 when p = 172.
Required: Determine function s(p)
[tex]s\ \alpha\ p[/tex]
Convert to equation
[tex]s = kp[/tex]
Where k is the constant of variation.
Make k the subject
[tex]k =\frac{s}{p}[/tex]
Substitute values for s and p
[tex]k =\frac{12.32}{172}[/tex]
Multiply by 100/200
[tex]k = \frac{1232}{17200}[/tex]
Simplify:
[tex]k =\frac{77}{1075}[/tex]
To get the function, we substitute 77/1075 for k in:[tex]s = kp[/tex]
[tex]s =\frac{77}{1075}p[/tex]
[tex]s =\frac{77p}{1075}[/tex]
Express as a function
[tex]s(p) =\frac{77p}{1075}[/tex]
