Final answer:
The data does not follow a simple exponential model, so we cannot determine the best exponential model that represents it.
Step-by-step explanation:
In order to determine the exponential model that best represents the data given, we need to see if there is a pattern or relationship between the values of x and f(x). We can examine the given data points to see if there is a common ratio between each successive value of f(x).
Let's calculate the ratio of each successive pair of f(x) values:
Ratio between -2 and -1: 128/27 = 4.74
Ratio between -1 and 0: 27/5 = 5.4
Ratio between 0 and 1: 5/1 = 5
Ratio between 1 and 2: 1/0.1 = 10
Since the ratios are not constant, the data does not follow a simple exponential model. Therefore, we cannot determine an exponential model that best represents the data given.