Question
Rachel found the following rate of change for the scenario represented in this table.
A 2-column table with 5 rows. Column 1 is labeled Time (hours) with entries 4, 5, 6, 7, 8. Column 2 is labeled Berries picked with entries 128, 181, 234, 287, 340.
What can you conclude from her work?
Check all that apply.
The scenario is represented by a linear function, since the rate of change is constant.
The scenario is represented by a nonlinear function, since the rate of change is constant.
The berries are picked at a constant rate of 53 per hour.
The berries are not picked at a constant rate.
A 2-column table with 5 rows. Column 1 is labeled Time (hours) with entries 4, 5, 6, 7, 8. Column 2 is labeled Berries picked with entries 128, 181, 234, 287, 340.
What can you conclude from her work?
Check all that apply.
The scenario is represented by a linear function, since the rate of change is constant.
The scenario is represented by a nonlinear function, since the rate of change is constant.
The berries are picked at a constant rate of 53 per hour.
The berries are not picked at a constant rate.
Answers
Answered by
GPT-4o mini
To analyze Rachel's findings regarding the rate of change in the given scenario, let's first compute the rate of change between the entries in the "Berries picked" column and the "Time" column.
1. **Calculating the Rate of Change:**
- From 4 hours to 5 hours: (181 - 128) / (5 - 4) = 53 berries/hour
- From 5 hours to 6 hours: (234 - 181) / (6 - 5) = 53 berries/hour
- From 6 hours to 7 hours: (287 - 234) / (7 - 6) = 53 berries/hour
- From 7 hours to 8 hours: (340 - 287) / (8 - 7) = 53 berries/hour
The rate of change is consistently 53 berries per hour throughout the time intervals provided.
2. **Conclusions:**
- The scenario is represented by a linear function, since the rate of change is constant. (This statement is true because the constant rate of change indicates a linear relationship.)
- The scenario is represented by a nonlinear function, since the rate of change is constant. (This statement is false; a constant rate of change indicates a linear function, not nonlinear.)
- The berries are picked at a constant rate of 53 per hour. (This statement is true, as we calculated the rate of change to be 53 berries/hour.)
- The berries are not picked at a constant rate. (This statement is false; as we established, the berries are picked at a constant rate of 53 berries/hour.)
### Summary:
From Rachel's work, the conclusions you can support are:
- The scenario is represented by a linear function, since the rate of change is constant.
- The berries are picked at a constant rate of 53 per hour.
1. **Calculating the Rate of Change:**
- From 4 hours to 5 hours: (181 - 128) / (5 - 4) = 53 berries/hour
- From 5 hours to 6 hours: (234 - 181) / (6 - 5) = 53 berries/hour
- From 6 hours to 7 hours: (287 - 234) / (7 - 6) = 53 berries/hour
- From 7 hours to 8 hours: (340 - 287) / (8 - 7) = 53 berries/hour
The rate of change is consistently 53 berries per hour throughout the time intervals provided.
2. **Conclusions:**
- The scenario is represented by a linear function, since the rate of change is constant. (This statement is true because the constant rate of change indicates a linear relationship.)
- The scenario is represented by a nonlinear function, since the rate of change is constant. (This statement is false; a constant rate of change indicates a linear function, not nonlinear.)
- The berries are picked at a constant rate of 53 per hour. (This statement is true, as we calculated the rate of change to be 53 berries/hour.)
- The berries are not picked at a constant rate. (This statement is false; as we established, the berries are picked at a constant rate of 53 berries/hour.)
### Summary:
From Rachel's work, the conclusions you can support are:
- The scenario is represented by a linear function, since the rate of change is constant.
- The berries are picked at a constant rate of 53 per hour.
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