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I wasn't sure how to word the question, but here is the whole problem!

The values of three functions are given in the tables below, rounded to two decimal places. Which function is which type? Choose from the options A, B, C, D, or E shown below where [a] a and [b] b are constants that may be positive, negative or zero.

    t   f(t)
    2.0 4.80
    2.2 5.81
    2.4 6.91
    2.6 8.11
    2.8 9.41
    3.0 10.8


    t   g(t)
    1.0 2.50
    1.2 4.32
    1.4 6.86
    1.6 10.24
    1.8 14.58
    2.0 20.00


    t  h(t)
    0.0 1.54
    1.0 1.69
    2.0 1.86
    3.0 2.04
    4.0 2.24
    5.0 2.46

A: [y=at^3+b]

B: [y=bt^2+a]

C: [y=ab^t]

D: [y=ax+b]

E: some other form different from the above three models

Thank you for any help or suggestions as to where to start

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1 Answer

The essence of the problem is to get a concrete feel for the rate at which certain functions grow. To approach this problem, think about how fast the function $y = ax + b$ "grows" compared to $y = bt^2 + a$. You may want to draw the graph of a specific function with specific numbers! That will help!

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