Questions: Solving Quadratic Equations Select the correct answer A coffee shop begins the day with 75 bagels and sells an average of 10 bagels each hour. Function b 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 ≤ x ≤ 75 B. -∞ ≤ x ≤ ∞ C. 0 ≤ x ≤ ∞ D. 0 ≤ x ≤ 7.5

Solving Quadratic Equations Select the correct answer A coffee shop begins the day with 75 bagels and sells an average of 10 bagels each hour. Function b 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 ≤ x ≤ 75 B. -∞ ≤ x ≤ ∞ C. 0 ≤ x ≤ ∞ D. 0 ≤ x ≤ 7.5
Transcript text: Solving Quadratic Equations Select the correct answer A coffee shop begins the day with 75 bagels and sells an average of 10 bagels each hour. Function $b$ 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. $-\infty \leq x \leq \infty$ C. $0 \leq x \leq \infty$ D. $0 \leq x \leq 7.5$
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Solution

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Solution Steps

Step 1: Determine the Relevant Domain

The function \( b(x) = 75 - 10x \) models the bagel inventory, where \( x \) is the number of hours after opening. The coffee shop starts with 75 bagels and sells 10 bagels per hour. The relevant domain for \( x \) is the time during which the shop has bagels to sell.

To find when the inventory reaches zero, set \( b(x) = 0 \):

\[ 75 - 10x = 0 \]

Solving for \( x \):

\[ 10x = 75 \\ x = 7.5 \]

Therefore, the relevant domain is \( 0 \leq x \leq 7.5 \).

Final Answer

D. \( 0 \leq x \leq 7.5 \)

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