Question

The given table shows the number of customers, c(x), in a diner when the diner has been open for x minutes.

x 30 45 60 75 90 105
c(x) 40 48 50 48 40 30

Which statement is supported by the table?

A.
The number of customers in the diner is increasing on the interval (30, 60).
B.
The number of customers in the diner is increasing on the interval (75, 105).
C.
The maximum number of customers in the diner is 105.
D.
The maximum number of customers in the diner is 60.

Answer 1

To determine which statement is supported by the table, let's analyze the data provided for the number of customers, c(x):

- At x = 30 minutes, c(30) = 40
- At x = 45 minutes, c(45) = 48
- At x = 60 minutes, c(60) = 50
- At x = 75 minutes, c(75) = 48
- At x = 90 minutes, c(90) = 40
- At x = 105 minutes, c(105) = 30

Now, let's check each statement:

A. The number of customers in the diner is increasing on the interval (30, 60).
- From 30 to 45 (40 to 48) and from 45 to 60 (48 to 50) the number of customers is increasing, so this statement is **true**.

B. The number of customers in the diner is increasing on the interval (75, 105).
- From 75 to 90 (48 to 40) and from 90 to 105 (40 to 30) the number of customers is decreasing, so this statement is **false**.

C. The maximum number of customers in the diner is 105.
- The maximum number of customers recorded in the table is 50 (at x = 60), so this statement is **false**.

D. The maximum number of customers in the diner is 60.
- The maximum number of customers recorded is 50 (at x = 60), not 60, so this statement is **false**.

Based on the analysis, the only statement supported by the table is:

**A. The number of customers in the diner is increasing on the interval (30, 60).**