Question

Find the constant difference for each table of values and use it to describe the data(linear, quadratic,or exponential

Answer 1

6. quadratic

7. linear

Explanation:

6. First differences are ...

• 5 -2 = 3
• 6 -5 = 1
• 5 -6 = -1
• 2 -5 = -3

Second differences are ...

• 1 -3 = -2
• -1 -1 = -2
• -3 -(-1) = -2

These are constant at -2, so the data are quadratic. The data can be described by y = 6-(x-3)^2.

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7. The x-values are evenly spaced (though decreasing). For our purpose, we can still look at the first differences of the table values in the order given. First differences are ...

• 8 -4 = 4
• 12 -8 = 4
• 16 -12 = 4
• 20 -16 = 4

These are constant at +4, so the data are linear. The data can be described by y = -4x +12.