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To determine that which of the transformations would be reasonable.

Since the students decided to draw a circle and see how many cheerios they could fit inside it. They alter the data to make it appear more linear before computing a linear regression line to observe the better outcome.
As a result, we must determine which of the following transformations they should attempt.
As a result, we can see that the pattern in the scatterplot looks like a quadratic function, implying that a graph of the type $y=a{x}^2+b$could be a good model. However, this indicates that the number of cheerios is equal to the square of the diameter up to a certain number of constants, and thus the proper transformation is to take the square root of the number of cheerios.

As a result, the transformation I is appropriate.
Similarly, the pattern of the given scatterplot resembles that of an exponential function, suggesting that it could be a model.
However, this indicates that the number of cheerios is the exponential of the diameter up to a constant, and that the logarithm of the number of cheerios is the appropriate transformation.
As a result, III is a suitable transition.
As a result, option (b) I and III is the correct answer.