Answer
(a).$m(t)=22\times2^{-t/1600}$
(b).$m(t)=22e^{-0.000433t}$
(c).$m(4000)=3.8891$
(d).$t=463.44$
Work Step by Step
$m(t)=m_0e^{-rt}$. Whereas,$m(t)$ is the mass of radioactive substance after time $t$, $m_0$ is the Initial mass of radioactive substance, $r=\frac{\ln 2}{h}$ is the rate of decay while $h$ is the half-life and $t$ is time.
(a).$m_0=22$
$m(t)=m_02^{-t/h}=22\times2^{-t/1600}$
(b). $r=\frac{\ln2}{h}=0.000433$
$m(t)=m_0e^{-rt}=22e^{-0.000433t}$
(c). $m(4000)=22\times2^{-4000/1600}=22\times2^{-2.5}=3.8891$
(d). $18=22\times e^{-0.000433t}$,
$0.8181=e^{-0.000433t}$,
$\ln(0.8181)=-0.000433t$,
$t=463.44$
