Forward Difference of Power

Theorem
$$\Delta c^{x} = (c-1)c^{x}$$

Corollary
$$\Delta 2^{x} = 2^{x}$$

Proof
From the definitions:

$$ $$ $$

Proof of corollary
$$\Delta 2^{x} = (2-1)2^{x} = 2^{x}$$