Question

select the correct answer. a coffee shop begins the day with 75 bagels and sells an average of 10 bagels each hour. function ( b(x) ) models the bagel inventory ( b(x) ), ( x ) hours after opening. ( b(x) = 75 - 10x ) if the coffee shop wants to make a graph of function ( b ), which values of ( x ) should it include on the graph to include the relevant domain within the context? a. ( 0 leq x leq 75 ) b. ( 0 leq x leq 8 ) c. ( -8 leq x leq 8 ) d. ( 0 leq x leq 7.5 )

Explanation:

Step1: Analyze the context

The function \( b(x) = 75 - 10x \) models the bagel inventory, where \( x \) is the number of hours after opening. The inventory \( b(x) \) can't be negative, so we set \( b(x)\geq0 \).

Step2: Solve the inequality

Set \( 75 - 10x\geq0 \).
Subtract 75 from both sides: \( - 10x\geq - 75 \).
Divide both sides by - 10 (and reverse the inequality sign): \( x\leq7.5 \).
Also, the number of hours \( x \) can't be negative, so \( x\geq0 \).

Step3: Determine the domain

Combining these, the domain of \( x \) in the context is \( 0\leq x\leq7.5 \).

Answer:

D. \( 0\leq x\leq7.5 \)