Answer
(a). $m(t)=9.97$ mg
(b).$t=138,934.76$ years
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.
$h=2.7\times10^5$,
(a). $m_0=10$, $t=1000$.
$m(t)=10\times2^{-1000/2.7\times10^5}=9.97$
(b). $7=10\times2^{-t/2.7\times10^5}$
$0.7=2^{-t/2.7\times10^5}$,
$\log 0.7=-t/2.7\times10^5 \log2$,
$t=138,934.76$ years