Question

Write out the first 5 outpouts of g(x)=2^x starting with G(1). If only you knew that the value of g(15) how would you determine g(16)?

Answer 1

The first 5 outputs are:

$\begin{array}{c|c}x&2^x\\1&2\\2&4\\3&8\\4&16\\5&32\end{array}$

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 $2^x$, the next value will be

$2^{x+1}=2^x\cdot 2$

So, again, we've shown that the next value is twice the previous one, so you have

$g(16)=2g(15)$