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State sales tax S is directly proportional to retail price p. An item that sells for 164 dollars has a sales tax of 12.32 dollars. Find a mathematical model that gives the amount of sales tax S in terms of the retail price p. Function: S(p) What is the sales tax on a 310 dollars purchase. Round to the nearest cent. The sales tax on a 310 dollar purchase is $ Question Help: D Video Submit Question

State sales tax S is directly proportional to retail price p. An item that sells for 164 dollars has a sales tax of 12.32 dollars. Find a mathematical model tha class=

Answer :

Answer:

Mathematical model: S(p) = 0.08p

[tex]S(p)=\frac{12.32p}{164}[/tex]

S(310) = $23.3

Explanation:

We're told from the question that sales tax, S, is directly proportional to retail price, p. This can be represented mathematically as seen below;

[tex]\begin{gathered} S\propto p \\ S=kp \end{gathered}[/tex]

where k = the constant of proportionality.

From the question, we're also told that when p = $164, S = $12.32.

Substituting the above values into our equation, we'll have;

[tex]\begin{gathered} 12.32=k\times164 \\ k=\frac{12.32}{164} \end{gathered}[/tex]

So our mathematical model can be represented as;

[tex]S(p)=\frac{12.32p}{164}[/tex]

Therefore, when p = $310, we can solve for S as seen below;

[tex]\begin{gathered} S(310)=0.08\times310 \\ S(310)=\text{ \$23.}3 \end{gathered}[/tex]

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