Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \( f(x+y)=f(x)f(y) \) for all \( x,y \in \mathbb{R} \). If \( f'(0)=4a \) and \( f \) satisfies \( f''(x)-3a f'(x)-f(x)=0, \, a>0 \), then the area of the region \( R=\{(x,y)\mid 0\le y\le f(ax),\,0\le x\le 2\} \) is:
