Answer
(a). $h=5$ days.
(b).$m(12)=0.1895$ or $18.95\%$ of the original amount
Work Step by Step
The formula for decaying radioactive substances is, $m(t)=m_0e^{-rt}$. Whereas, $m_0$ is the Initial mass, $r$ is rate, $m(t)$ is the mass after $t$ years. Or $m(t)=m_02^{-t/h}$, Whereas $h$ is the half-life.
$m_0=1$, $m(8)=0.33$,
(a).$m(8)=1\times2^{-8/h}=0.33$,
$2^{-8/h}=0.33$,
$\frac{-8}{h}\log2=\log 0.33$,
$h=5$ days.
(b).$m(12)=1\times2^{-12/5}=0.1895$ or $18.95\%$ of the original amount
