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Question 7 of 10

Karen owns a seafood restaurant. She orders trout from an online retailer. Each pound of trout costs [tex]\$28[/tex], and the company charges a [tex]\$4[/tex] fee for shipping the order. However, if Karen orders 10 or more pounds, the trout costs only [tex]\$22[/tex] per pound, but the shipping fee is [tex]\$8[/tex].

Which piecewise function models the cost of [tex]x[/tex] pounds of trout?

A. [tex]f(x)=\left\{\begin{array}{l}22x+8, \, 0 \ \textless \ x \ \textless \ 10 \\ 28x+4, \, x \geq 10\end{array}\right.[/tex]

B. [tex]f(x)=\left\{\begin{array}{l}28x+4, \, 0 \ \textless \ x \ \textless \ 10 \\ 22x+8, \, x \geq 10\end{array}\right.[/tex]

C. [tex]f(x)=\left\{\begin{array}{l}22x+8, \, 0 \ \textless \ x \leq 10 \\ 28x+4, \, x \ \textgreater \ 10\end{array}\right.[/tex]

D. [tex]f(x)=\left\{\begin{array}{l}28x+4, \, 0 \ \textless \ x \leq 10 \\ 22x+8, \, x \ \textgreater \ 10\end{array}\right.[/tex]



Answer :

GinnyAnswer
Let's analyze the conditions given for determining the total cost of trout for Karen's seafood restaurant.

1. If Karen orders less than 10 pounds of trout:
- Each pound costs \[tex]$28. - There is an additional shipping fee of \$[/tex]4.
- Thus, the total cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] pounds when [tex]\( 0 < x < 10 \)[/tex] is given by:
[tex]\[ C = 28x + 4 \][/tex]

2. If Karen orders 10 pounds or more of trout:
- Each pound costs \[tex]$22. - There is an additional shipping fee of \$[/tex]8.
- Thus, the total cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] pounds when [tex]\( x \geq 10 \)[/tex] is given by:
[tex]\[ C = 22x + 8 \][/tex]

We need to construct the piecewise function [tex]\( f(x) \)[/tex] based on these conditions.

The correct piecewise function is:
[tex]\[ f(x) = \begin{cases} 28x + 4 & \text{if } 0 < x < 10 \\ 22x + 8 & \text{if } x \geq 10 \end{cases} \][/tex]

Comparing this with the options provided, we see that option B matches the conditions exactly:

[tex]\[ f(x) = \begin{cases} 28x + 4 & \text{if } 0 < x < 10 \\ 22x + 8 & \text{if } x \geq 10 \end{cases} \][/tex]

Thus, the correct answer is:
[tex]\[ B \][/tex]