Question

What rule(function) does the table below represents?

Answer 1

The function that represents the table is
`f(x) = 15\cdot 2^(x+1)`.

Explanation:

The table represents the following rule: A function whose initial values are
`x = -1` and
`f(x) = 15`, as for each increase of the input by -1, the output is doubled. Mathematically speaking, we construct the following geometric progression:

`f(x) = a_(o)\cdot 2^{x-x_(o)}` (1)

Where:

`a_(o)` - Initial output.

`x_(o)` - Initial input.

`x` - Input

`f(x)` - Output

If we know that
`a_(o) = 15` and
`x_(o) = -1`, then the function that represents the table is:

`f(x) = 15\cdot 2^(x+1)`