Radioactive decay follows first-order kinetics. The amount of substance remaining ($N$) after $n$ half-lives is given by the formula:

$N = \frac{N_0}{2^n}$

where $N_0$ is the initial amount. Given: Half-life, $t_{1/2} = 4 \text{ days}$ Total time, $t = 16 \text{ days}$ Number of half-lives, $n = \frac{t}{t_{1/2}} = \frac{16}{4} = 4$

Therefore, the quantity of matter remaining undecayed is: $N = \frac{N_0}{2^4} = \frac{N_0}{16}$

So, $\frac{1}{16}$th of the initial quantity remains.