Answer:
The function that represents the table is [tex]f(x) = 15\cdot 2^{x+1}[/tex].
Step-by-step explanation:
The table represents the following rule: A function whose initial values are [tex]x = -1[/tex] and [tex]f(x) = 15[/tex], as for each increase of the input by -1, the output is doubled. Mathematically speaking, we construct the following geometric progression:
[tex]f(x) = a_{o}\cdot 2^{x-x_{o}}[/tex] (1)
Where:
[tex]a_{o}[/tex] - Initial output.
[tex]x_{o}[/tex] - Initial input.
[tex]x[/tex] - Input
[tex]f(x)[/tex] - Output
If we know that [tex]a_{o} = 15[/tex] and [tex]x_{o} = -1[/tex], then the function that represents the table is:
[tex]f(x) = 15\cdot 2^{x+1}[/tex]
