Growth of Plant Sample A
Time (days) Height (in.)
1 6
2 12
3 18
4 24
5 30 Growth of Plant Sample B
Time (days) Height (in.)
1 2
2 5
3 10
4 17
5 26
Compare the data for the growth of two plant samples. How can you determine which data set is linear?
A) Sample B has linear data because it increases as a slower rate.
B) Sample A has linear data because it has a constant rate of change.
C) Neither sample has linear data because the samples start at different heights.
D) Both samples have linear data because as x increases, y increases.
b?
Yes, b is correct.
Well, let's see. If we look at the data, we can observe that the height of Sample A increases by 6 inches per day consistently. However, the height of Sample B does not increase at a constant rate. It starts off slow, then speeds up, and then slows down again. So, it seems like Sample A has a constant rate of change, which is one of the characteristics of linear data. Therefore, I would go with option B) Sample A has linear data because it has a constant rate of change.
B) Sample A has linear data because it has a constant rate of change.
In Sample A, the height increases by 6 inches every day. This constant rate of change indicates a linear relationship between the time (days) and the height (inches).
To determine which data set is linear, we need to examine the rate of change between the variables (time and height). In a linear relationship, the rate of change between the variables remains constant.
Looking at Sample A, we can determine its rate of change by calculating the difference in height between consecutive time points. The differences are as follows:
- From day 1 to day 2: 12 - 6 = 6
- From day 2 to day 3: 18 - 12 = 6
- From day 3 to day 4: 24 - 18 = 6
- From day 4 to day 5: 30 - 24 = 6
As you can see, the height difference between consecutive time points is always 6. Since the rate of change remains constant (6), we can conclude that Sample A has linear data.
Now, let's analyze Sample B in the same way:
- From day 1 to day 2: 5 - 2 = 3
- From day 2 to day 3: 10 - 5 = 5
- From day 3 to day 4: 17 - 10 = 7
- From day 4 to day 5: 26 - 17 = 9
In this case, the height difference between consecutive time points is not constant. It varies (3, 5, 7, 9), indicating a non-linear relationship.
Based on these calculations, we can determine that Sample A has linear data because it has a constant rate of change. Therefore, the correct answer is B) Sample A has linear data because it has a constant rate of change.