Answer
(a) $3.8$ days
(b) $8.8$ days
Work Step by Step
(a) Use the exponential decay model $m(t)=m_0\cdot 2^{-t/h}$ and the given conditions $m(3)=0.58m_0, t=3$, we have $0.58m_0=m_0\cdot 2^{-3/h}$ which gives $h=-3/(log_20.58)\approx3.8$ days
(b) Let $m(t)=0.2m_0$, we have $0.2m_0=m_0\cdot 2^{-t/3.8}$ which gives $t=-3.8\times log_20.2\approx8.8$ days
