The help desk is keeping track of the number of minutes the average caller spends on hold.

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ Average Time on Hold with Help Desk } \\
\hline Week & \begin{tabular}{c}
Average Time on Hold \\
(Minutes)
\end{tabular} \\
\hline 1 & 7 \\
\hline 2 & 5 \\
\hline 3 & 3 \\
\hline 4 & 2 \\
\hline 5 & 3 \\
\hline 6 & 5 \\
\hline
\end{tabular}

According to the table, during which interval did the average time spent on hold increase?

A. week 1 to week 3
B. week 1 to week 4
C. week 4 to week 6
D. week 3 to week 5

Let's analyze the average time on hold in the given intervals to determine when the average time spent on hold increased.

### Interval from Week 1 to Week 3:
- Average time on hold in Week 1: 7 minutes
- Average time on hold in Week 3: 3 minutes

Change in time [tex]$ \Delta t_{1\rightarrow3} = 3 - 7 = -4 $[/tex]

Since the change is negative, the time on hold decreased between Week 1 and Week 3.

### Interval from Week 1 to Week 4:
- Average time on hold in Week 1: 7 minutes
- Average time on hold in Week 4: 2 minutes

Change in time [tex]$ \Delta t_{1\rightarrow4} = 2 - 7 = -5 $[/tex]

Since the change is negative, the time on hold decreased between Week 1 and Week 4.

### Interval from Week 4 to Week 6:
- Average time on hold in Week 4: 2 minutes
- Average time on hold in Week 6: 5 minutes

Change in time [tex]$ \Delta t_{4\rightarrow6} = 5 - 2 = 3 $[/tex]

Since the change is positive, the time on hold increased between Week 4 and Week 6.

### Interval from Week 3 to Week 5:
- Average time on hold in Week 3: 3 minutes
- Average time on hold in Week 5: 3 minutes

Change in time [tex]$ \Delta t_{3\rightarrow5} = 3 - 3 = 0 $[/tex]

Since the change is zero, the time on hold did not increase between Week 3 and Week 5.

Based on this analysis, the interval during which the average time spent on hold increased is:

- Week 4 to Week 6