Answer
(a) $m(t)=150e^{-0.0004359t}$
(b) $97.0$mg
(c) $2520$ years
Work Step by Step
(a) Given $h=1590,m_0=150$ and use the radioactive decay model, we have $m(t)=m_0e^{-rt}$
where $r=ln2/h=ln2/1590\approx0.0004359$ and the model becomes $m(t)=150e^{-0.0004359t}$
(b) Let $t=1000$, we have $m(1000)=150e^{-0.0004359\times1000}\approx97.0$mg
(c) Given $m(t)=50$, we have $150e^{-0.0004359t}=50$ which gives $t=-ln(\frac{50}{150})/0.0004359\approx2520$ years
