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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]
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:
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