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) = 75 – 10x hours after opening.
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. -∞ ≤ x ≤ ∞
B. 0 ≤ x ≤ 7.5
C. 0 ≤ x ≤ ∞
D. 0 ≤ x ≤ 75
The correct answer is B. 0 ≤ x ≤ 7.5.
Explanation: The function b(x) = 75 – 10x represents the inventory of bagels over time. The coffee shop starts with 75 bagels and sells 10 bagels each hour. To find out how long the shop will keep selling bagels until they run out, you set b(x) = 0:
75 – 10x = 0
10x = 75
x = 7.5
Thus, the relevant domain for x is from 0 hours to 7.5 hours after opening, as this represents the time until the inventory is depleted.