Question

question 1 · 1 point which type of model is most appropriate for the following data?

x	y
1	2.63
2	5.85
3	7.74
4	8.92
5	10
6	10.95
7	11.49
8	12.09

Explanation:

Step1: Observe the rate of change

As $x$ increases, the rate of change of $y$ is decreasing. For example, from $x = 1$ to $x=2$, $y$ changes by $5.85 - 2.63=3.22$, from $x = 2$ to $x = 3$, $y$ changes by $7.74 - 5.85 = 1.89$.

Step2: Recall model - rate of change characteristics

In a linear model, the rate of change is constant. In an exponential model, the rate of change increases over time. In a logarithmic model, the rate of change decreases as the independent variable ($x$) increases, which matches the behavior of the given data.

Answer:

A logarithmic model is most appropriate.