Consider the following equation with an unknown function $y(x)$: $$\Delta y(x)=y(x).$$ 1. Expand the left-hand side of this equation using the definition of $\Delta$ (from Honors HW1).

2. Solve the resulting equation from Problem 1 for $y(x)$. (note: you will get a $y(x+1)$ on the "other side").

3. If $y(0)=1$, then use the formula you found in Problem 2 to find $y(1)$, $y(2)$, and $y(3)$.

4. If $y(0)=2$, then use the formula you found in Problem 2 to find $y(1)$, $y(2)$, and $y(3)$.

5. Let $f(t)=2^t$. Compute $\Delta f(t)$. Can you express $\Delta f(t)$ in terms of $f(t)$?