To find the average rate of change for the data from the 2nd hour to the 6th hour, let's analyze it step-by-step.
First, we need to identify the sales values at the 2nd hour and the 6th hour. According to the data given:
- Sales at the 2nd hour: 50 units
- Sales at the 6th hour: 150 units
Next, we calculate the total change in sales between these two hours. We subtract the sales value at the 2nd hour from the sales value at the 6th hour:
[tex]\[ \text{Change in sales} = \text{Sales at 6th hour} - \text{Sales at 2nd hour} \][/tex]
[tex]\[ \text{Change in sales} = 150 - 50 \][/tex]
[tex]\[ \text{Change in sales} = 100 \text{ units} \][/tex]
Now, we need to determine the total number of hours between the 2nd hour and the 6th hour:
[tex]\[ \text{Total hours} = 6 - 2 \][/tex]
[tex]\[ \text{Total hours} = 4 \text{ hours} \][/tex]
To find the average rate of change, we divide the total change in sales by the total number of hours:
[tex]\[ \text{Average rate of change} = \frac{\text{Change in sales}}{\text{Total hours}} \][/tex]
[tex]\[ \text{Average rate of change} = \frac{100 \text{ units}}{4 \text{ hours}} \][/tex]
[tex]\[ \text{Average rate of change} = 25 \text{ units per hour} \][/tex]
Hence, the average rate of change in sales from the 2nd hour to the 6th hour is 25 units per hour.
