What are the missing values, and what is the equation for the table

9514 1404 393

Step-by-step explanation:

Two points are not sufficient to define a graph, so the equation could be anything that gives the listed values.

We note that the given y-values are powers of 2. Specifically, they are 2^4 and 2^8. These powers differ by 4, just as the corresponding x-values differ by 4. This suggests an exponential equation might be good fit:

  y = 2^(x+3)

Simplified, this is ...

  y = 8·2^x . . . . . exponential equation for table values

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Alternate solution

Often, when only two points are given, a linear function is indicated. We can use the two given points in the 2-point form of the equation for a line to find what the linear equation might be.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (256 -16)/(5 -1)(x -1) +16 . . . . with values filled in

  y = 240/4(x -1) +16 . . . . . . . . . . . find the ratio

  y = 60x -60 +16 . . . . . . . . . . . . . eliminate parentheses

  y = 60x -44 . . . . . linear equation for table values

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The two answers we looked at here are shown in the attached table. There are an infinite number of other possibilities.

step-by-step explanation:

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step-by-step explanation: