The first 5 outputs are:
[tex]\begin{array}{c|c}x&2^x\\1&2\\2&4\\3&8\\4&16\\5&32\end{array}[/tex]
As you can see, the outputs keep doubling each time we increment x by 1.
This can be written formally, observing that if you know the value of [tex]2^x[/tex], the next value will be
[tex]2^{x+1}=2^x\cdot 2[/tex]
So, again, we've shown that the next value is twice the previous one, so you have
[tex]g(16)=2g(15)[/tex]
