| x | -9.8 | -0.9 | 5.2 | 8.8 |
|---|---|---|---|---|
| y | 0.12 | 2.43 | 18.46 | 68.4 |
Which of the following equations best models the data in the table above?
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The correct answer is D.
One way to determine which of the equations best models the data in the table is to use a calculator that has a statistics mode to compute an exponential regression for the data.
The specific steps to be followed depend on the model of calculator, but can be summarized as follows: Enter the statistics mode, edit the list of ordered pairs to include only the four points given in the table and perform an exponential regression. The coefficients are, approximately, 
for the constant and 
for the base, which indicates that the exponential equation 
is the result of performing the exponential regression. If the calculator reports a correlation, it should be a number that is very close 
, to which indicates that the data very closely matches the exponential equation. Therefore, of the given models, best fits the data.
Alternatively, without using a calculator that has a statistics mode, one can reason about the data given in the table.
The data indicates that as 
increases, 
increases; thus, options A and B cannot be candidates for such a relationship. Evaluating options C, D, and E at 
shows that option D is the one that gives a value of that is closest to 
. In the same way, evaluating options C, D, and E at each of the other given data points shows that option D is a better model for that one data point than either option C or option E. Therefore, is the best of the given models for the data.