Answer
(a).$m_0=12$
(b).$m(t)=12\times2^{-t/4}$
(c). $m(3)=7.14$
(d). $t=25.3$
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.
$h=4$ days, $t=20$, $m(20)=0.375$
(a). $0.375=m_02^{-5}$,
$m_0=12$
(b).$m(t)=12\times2^{-t/4}$
(c). $m(3)=12\times2^{-3/4}=7.14$
(d). $0.15=12\times2^{-t/4}$,
$0.0125=2^{-t/4}$,
$\log 0.0125=\frac{-t}{4}\log2$,
$t=25.3$
