Select the correct answer.

Jenny is tracking the monthly sales totals for her boutique. The given piecewise function represents the boutique's monthly sales, in dollars, where [tex]$x$[/tex] represents the number of months since Jenny began tracking the data.

[tex]f(x)=\left\{\begin{array}{ll}4,000(1.1)^x, & 0 \leq x\ \textless \ 3 \\ 100 x+5,024, & 3 \leq x\ \textless \ 6 \\ -x^2+5 x+5,630, & 6\ \textless \ x \leq 8\end{array}\right.[/tex]

What were the boutique's monthly sales when Jenny first began tracking the data?

A. [tex]$4,400[/tex]
B. [tex]$5,616[/tex]
C. [tex]$5,324[/tex]
D. [tex]$4,000[/tex]

We are given a piecewise function for monthly sales and need to find the sales at x = 0 .
Since 0 ≤ x < 3 , we use the first part of the piecewise function: f ( x ) = 4000 ( 1.1 ) x .
Substitute x = 0 into the equation: f ( 0 ) = 4000 ( 1.1 ) 0 = 4000 ∗ 1 = 4000 .
The boutique's monthly sales when Jenny first began tracking the data were $4 , 000 ​ .

Explanation

Understanding the Problem We are given a piecewise function that represents the monthly sales of a boutique. We want to find the sales when Jenny first began tracking the data. This means we need to find the value of the function when x = 0 , where x is the number of months since Jenny began tracking the data.

Choosing the Correct Piece The piecewise function is defined as:


$f(x)=\left{\begin{array}{ll}4,000(1.1)^x, & 0 \leq x<3 \ 100 x+5,024, & 3 \leq x<6 \ -x^2+5 x+5,630, & 6

Answered by GinnyAnswer | 2025-07-05