Deriving the formula from a graph

[adjacent]

So,here we have a graph.For every unit of 1(x axis),the unit of the previous y-axis is multiplied.
Like this.
(0,2),(1,4),(2,8),(3,16)...
I don't know how the formula will be,and had never seen this kind of graph.
The y seems to be a geometric sequence,on which we can use, ## ar^(n-1) ## .r is 2.a is 2
So 2 x 2^(n-1)
n is the value of x.For every value of x,we can now find the value of y.
So how can we find the general formula of the graph?Is it ## y=2 x 2^(x-1) ## ? I don't think so,If the x values started with 1,it's possible.

I don't know why LaTeX is not working,Help please.

 

[LCKurtz]

Your pairs are $(n, 2^{n+1})$ for $n=0,1,2,...$.

 

[adjacent]

How did you derive that?What could be the general formula? $y=2^{x+1}$ ?

 

[LCKurtz]

Your pairs are $(n, 2^{n+1})$ for $n=0,1,2,...$.

How did you derive that?What could be the general formula? $y=2^{x+1}$ ?

Yes. You already noticed the $y$ values were powers of $2$. So it was just a matter of adjusting the exponent to make the $y$ value agree with the $x$ value.

 

[adjacent]

Thanks, (lol I take reliable and cheap)