Answer
(a) $m(t)=3\cdot 2^{-t/10}$
(b) $m(t)=3e^{-0.0693t}$
(c) $0.047$g
(d) $3.6$ minutes
Work Step by Step
(a) Given $h=10s, m_0=3g$, the function becomes
$m(t)=3\cdot 2^{-t/10}$
(b) In this case $m(t)=3e^{-rt}$ and half life $10s$ gives $m(10)=m_0/2=3/2=1.5$,
so we have $1.5=3e^{-10r}$, solve for $r$ we get $r=-ln(1.5/3)/10=0.0693$
The function becomes $m(t)=3e^{-0.0693t}$
(c) Let $t=1min=60s$, use the formula in (a), we have
$m(60)=3\times2^{-60/10}\approx0.047$g
(d) Let $m(t)=1\mu g=10^{-6}g$, use the formula in (b), we have
$3e^{-0.0693t}=10^{-6}$, solve for $t$ to get $t=-ln(10^{-6}/3)/0.0693\approx215.2s\approx3.6$ minutes