Explain the transformation needed to convert the following data to a linear data set.

{(1, 0.98), (2, 1.39), (3, 1.71), (4, 1.98), (5, 2.22), (6, 2.43)} (6 points)

To convert the given data set to a linear data set, we need to find a transformation that would make the relationship between the x-values and y-values linear.

Let's start by plotting the given data points on a graph to visualize their relationship:

{(1, 0.98), (2, 1.39), (3, 1.71), (4, 1.98), (5, 2.22), (6, 2.43)}

From the graph, we can see that the data points do not fall on a straight line. Therefore, we need to find a transformation that will straighten the line.

One common transformation used to linearize data is taking the logarithm. In this case, we can take the logarithm of the y-values to see if it results in a linear relationship.

Let's take the natural logarithm (ln) of the y-values and plot the transformed data points:

{(1, ln(0.98)), (2, ln(1.39)), (3, ln(1.71)), (4, ln(1.98)), (5, ln(2.22)), (6, ln(2.43))}

Now, let's plot these transformed data points on a graph. If the transformation is successful, the data points should fall on a straight line.

If the transformed data points form a straight line, then the transformation is successful, and we have converted the original data set into a linear data set.