1. Sketch the curve

   $$y=|2e^x-4|$$

   indicating the coordinates of any intersections with the axes, and the equations of any asymptotes.

2. Solve the equation

   $$|2e^x-4|=3$$

Start by sketching $y=2e^x$, then $y=2e^x-4$, then $y=|2e^x-4|$.

If the roots are $\alpha$ and $\beta$, then $|\beta -\alpha |$ can be expressed as

where $k\in \mathbb{N}$ is prime. Give the value of $k$.