Answer:
Quadratic (2nd degree)
Explanation:
You want to fill the table with ratios, first- and second-differences to determine the type of function that M(x) is.
Ratios
To determine whether the function is exponential, we need to see if the ratios of successive terms are constant. The first two ratios will tell:
- 120/20 = 6
- 420/120 = 7/2 . . . . not the same as 6
The function is not an exponential function.
First differences
If the function is linear, the first differences will be constant. The first three first differences are ...
- 120 -20 = 100
- 420 -120 = 300
- 920 -420 = 500
300 ≠ 100, so we know the first differences are not constant and the function is not a linear function.
Second differences
The differences of the first differences are ...
- 300 -100 = 200
- 500 -300 = 200
The second differences are constant with a value of 200. When the second differences are constant, the function is of second degree. Another name for a second-degree function is quadratic function.
The function is a quadratic function (2nd degree).
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Additional comment
You may be expected to completely fill the table. The remaining blanks are filled with the same computations as the blanks above them. As you can see, it is not necessary to completely fill the table in order to answer the question as to the function's type.
To avoid some of the tedium, you could enter the values and formulas in a spreadsheet.
The first attachment shows a calculator finding the ratios.
The second attachment shows the calculator finding the differences. The same L1 list is used.
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