Out of the following data sets, which is best described as having a positive exponential relationship?(1 point)
A.x 0 1 2 3 4 5
y 0.6 0.9 1.5 2.3 2.9 4.9
B.x 0 1 2 3 4 5
y 0.1 0.5 1.1 1.4 2 2.5
C.x 0 1 2 3 4 5
y 3.4 4.5 6.2 8.5 9.1 8.6
D.x 0 1 2 3 4 5
y 7 4.3 6.2 7.4 8.8 10.9
AAAaannndd the bot gets it wrong yet again!
C cannot be right, since f(5) < f(4)
To determine which data set has a positive exponential relationship, we need to look for a pattern where the y-values increase rapidly as the x-values increase.
Let's analyze each data set:
A. As x increases from 0 to 5, the corresponding y-values increase significantly. The rate of increase appears to be exponential, with larger differences between consecutive y-values. Therefore, data set A can be described as having a positive exponential relationship.
B. In data set B, the y-values increase, but the rate of increase is not as rapid as in data set A. The differences between consecutive y-values are smaller, indicating a slower rate of growth. Therefore, data set B does not have a positive exponential relationship.
C. Data set C also shows an increase in y-values, but the rate of increase is not consistently rapid. Some y-values increase significantly, while others increase moderately. Therefore, data set C does not have a positive exponential relationship.
D. In data set D, the y-values do not consistently increase as the x-values increase. The y-values show some fluctuations and do not demonstrate a clear exponential growth pattern. Therefore, data set D does not have a positive exponential relationship.
Therefore, the data set that is best described as having a positive exponential relationship is data set A.
To determine which data set has a positive exponential relationship, we need to look for a pattern in the y-values as the x-values increase.
In an exponential relationship, the y-values increase or decrease at an increasing rate as the x-values increase. This means that the rate of change of the y-values is not constant but gets larger or smaller as x increases.
Let's analyze each data set:
A. The y-values in this data set seem to be increasing at an increasing rate as x increases. For example, the difference between y-values for adjacent x-values is as follows: 0.3, 0.6, 0.8, 0.6, and 2.0. This pattern suggests a positive exponential relationship.
B. The y-values in this data set do increase as x increases, but the difference between the y-values for adjacent x-values is not consistently increasing. This data set does not exhibit a positive exponential relationship.
C. The y-values in this data set do increase as x increases, but the difference between the y-values for adjacent x-values is not consistently increasing. This data set does not exhibit a positive exponential relationship.
D. The y-values in this data set seem to increase at a relatively constant rate as x increases. For example, the difference between y-values for adjacent x-values is as follows: -2.7, 1.9, 1.2, 1.4, and 2.1. This pattern suggests a linear relationship, not an exponential relationship.
Based on this analysis, only data set A shows a positive exponential relationship.
C.x 0 1 2 3 4 5
y 3.4 4.5 6.2 8.5 9.1 8.6