Question

worried about going over her storage limit, ling monitored the number of undeleted voicemail messages stored on her phone each day. voicemail messages on ling’s phone. according to the graph, what was the rate of change between sunday and wednesday? round your answer to the nearest tenth. voicemail messages per day

Explanation:

Step1: Identify points

Sunday: (0, 0), Wednesday: (3, 10) (assuming Wednesday is 3 days after Sunday, and voicemail count is 10? Wait, graph: Sunday is 0, Wednesday has a point at 10? Wait, the graph: Sunday (0,0), then Wednesday (3,10)? Wait, maybe Sunday is day 0, Monday day 1, Tuesday day 2, Wednesday day 3. The voicemail on Sunday: 0, Wednesday: 10? Wait, no, looking at the graph: the vertical axis is voicemail messages, horizontal is day (Sunday, Monday, Tuesday, Wednesday, Thursday). Sunday: 0, Wednesday: let's see, the line from Sunday (0,0) to Wednesday (3,10)? Wait, no, the graph shows Sunday at 0, then a point on Wednesday at 6? Wait, maybe I misread. Wait, the problem: rate of change between Sunday and Wednesday. Rate of change is (change in y)/(change in x). Let's assume Sunday is day 0, Wednesday is day 3 (since Sunday, Monday, Tuesday, Wednesday: 3 days later). From the graph, Sunday: 0 voicemails, Wednesday: 10? Wait, no, the graph: the first point (Sunday) is (0,0), then Wednesday has a point at (3,10)? Wait, maybe the y-axis: Sunday is 0, Wednesday is 10? Wait, no, the graph's vertical axis: the numbers are 0,6,7,8,9,10,11,12,13. Wait, Sunday is at 0, Wednesday's point is at 6? Wait, maybe I messed up. Wait, the problem says "rate of change between Sunday and Wednesday". Let's check the coordinates. Let's define x as day (Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4). y is voicemail messages. Sunday: (0, 0). Wednesday: (3, 10)? Wait, no, the graph: the line from Sunday (0,0) to Wednesday (3,10)? Wait, no, looking at the graph, the first segment: Sunday to Wednesday? Wait, no, the graph has Sunday at 0, then a point on Wednesday at 10? Wait, maybe the correct points: Sunday (0, 0), Wednesday (3, 10). Then change in y: 10 - 0 = 10. Change in x: 3 - 0 = 3. Rate of change: 10/3 ≈ 3.3? Wait, no, maybe the Wednesday point is at 6? Wait, the graph's vertical axis: the first mark after 0 is 6? Wait, maybe the y-axis is labeled with 0,6,7,8,9,10,11,12,13. So Sunday is at 0, Wednesday is at 6? Wait, that doesn't make sense. Wait, maybe the days: Sunday, Monday, Tuesday, Wednesday, Thursday. So from Sunday (day 0) to Wednesday (day 3). The voicemail on Sunday: 0, on Wednesday: 10? Wait, the graph shows a line from Sunday (0,0) to Wednesday (3,10)? Wait, no, the graph has a point on Sunday at (0,0), then a point on Wednesday at (3,10)? Wait, maybe I misread. Wait, the problem says "rate of change between Sunday and Wednesday". Let's use the formula for rate of change: (y2 - y1)/(x2 - x1). Let's assume Sunday is x=0, y=0. Wednesday is x=3 (since 3 days later: Sunday, Monday, Tuesday, Wednesday), y=10. Then rate of change is (10 - 0)/(3 - 0) = 10/3 ≈ 3.3. Wait, but maybe the Wednesday point is at 6? Wait, the graph's vertical axis: the first mark after 0 is 6, then 7,8,9,10,11,12,13. So Sunday: (0,0), Wednesday: (3,10)? Wait, no, the line from Sunday (0,0) to Wednesday (3,10) is increasing, then another line. Wait, maybe the correct points: Sunday (0, 0), Wednesday (3, 10). Then rate of change is 10/3 ≈ 3.3. Wait, but let's check again. The problem says "round to the nearest tenth". So 10 divided by 3 is approximately 3.3.

Step1: Determine coordinates

Let Sunday be \( x_1 = 0 \), \( y_1 = 0 \). Wednesday is \( x_2 = 3 \) (3 days after Sunday), \( y_2 = 10 \) (from graph).

Step2: Calculate rate of change

Rate of change formula: \( \frac{y_2 - y_1}{x_2 - x_1} \)
Substitute values: \( \frac{10 - 0}{3 - 0} = \frac{10}{3} \approx 3.3 \)

Answer:

\( 3.3 \) voicemail messages per day