Answer:
- linear
- additively
- common difference
- about 240.12
Explanation:
Given the values in the table, you want to know if they represent a linear or exponential relation, along with the common difference or ratio, as applicable.
Changes
The first attachment shows the differences and ratios between successive table values. Neither the differences nor the ratios are constant. The wide variation in ratios and the relatively smaller variation in differences suggests the table is best modeled by a linear function.
Changes when the function is linear are additive. That is, the function values have a common difference.
Common difference
The average difference between table values is (949.92 -229.44)/3 = 240.16. A linear regression analysis gives a slope of 240.12 as the "best fit" to the table values.
You can see from the first attachment that the differences are not constant, so there isn't really a common difference. The difference is approximately 240.12.
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Additional comment
The second attachment shows linear and an exponential regression applied to this data. The residuals are much smaller for the linear approximation.
The slope of the line (common difference) is estimated at 240.12 using the regression formula. This makes the mean square residuals a minimum. As we show above, this slope is different (slightly lower) than the slope of the line through the first and last data points.