Question

What rule(function) does the table below represents?

Answer 1

Answer:

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

Step-by-step 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:

$f(x) = 15\cdot 2^{x+1}$