Algebra Table of value (please help)

Question

Look for a pattern in the table of values.

x | -3 | -2 | -1 | 0 | 1 | 2 |

y | 32 | 16 | 8 | 4 | 2 | 1 |

A. Which model (linear, exponential, or quadratic) best describes the data?

B. Write an equation for the function that models the data.

Answer 1

Because the x is given with constant intervals, we can identify the functionality by looking at the change in y:

1) linear function: change in y is constant

2) quadratic function: change in y is linear

3) exponential: change in y is multiplicative

The change is 16, 8 ,4, 2, 1 which is case 3 (The multiplier is 1/2, so we can consider a function

of the form

y = a(2)^-bx

For the point (0,4) we get 4 = a(1) or a = 4

Picking another point: (say (1,4) we obtain 2 = 4(2)^-b 1/2 = 2^-b b = 1

y = 2(2)^-x is the function (Test to make sure with -3... y = 4*(2)³ = 32)

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