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March 26, 2017

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Which kind of function best models the data in the table? Use differences or ratios.

x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

A.linear
B.quadratic
C.exponential
D.none of the above
I think it is C...?

  • Algebra - ,

    first difference table

    6.8 - 1.7 = 5.1

    27.2 - 6.8 = 20.4

    108.8 - 27.2 = 81.6

    435.2 - 108.8 = 326.4
    so not linear

    second differences
    20.4 - 5.1 = 15.3
    81.6 - 20.4 = 61.2
    326.4 - 81.6 = 244.8
    so not quadratic

    try ratios
    6.8/1.7 = 4
    27.2/6.8 = 4

    ah hah ! constant ratio of 4

  • Algebra - ,

    looks like
    y = 1.7(4)^x

  • Algebra - ,

    sorry about repeat
    yes, 1.7 * 4^x

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