Question

explanation: the independent variable is b, and the dependent variable is f(b). part b let f(b) be the profit the band makes on sales of bracelets, where b is the number of bracelets sold. write a function modeling the relationship. (hint: profit = selling price - cost price) enter the correct answer in the box. f(b) =

Explanation:

Step1: Define Profit Formula

Profit = (Selling Price per Bracelet - Cost Price per Bracelet) × Number of Bracelets Sold. Let selling price per bracelet be \( s \), cost price per bracelet be \( c \). Then profit for \( b \) bracelets is \( (s - c) \times b \).

Step2: Form Function \( f(b) \)

Let \( f(b) \) represent profit. So \( f(b)=(s - c)b \), or in general, if we consider per - bracelet profit as a constant (say \( p = s - c \)), then \( f(b)=pb \) (where \( p \) is profit per bracelet). If we don't have specific values for \( s \) and \( c \), the function is \( f(b)=( \text{Selling Price per Bracelet}-\text{Cost Price per Bracelet}) \times b \). Assuming we can write it as \( f(b)=(s - c)b \) (or with actual numbers if given, but since not given, we use the formula structure).

Answer:

\( f(b)=(s - c)b \) (or if we assume per - unit profit is a constant \( k \), \( f(b)=kb \), where \( k=\text{Profit per bracelet}=\text{Selling Price}-\text{Cost Price} \))