Answer
(a). $m(t)=150\times2^{-t/1590},$
(b). $m(1000)=96.998$
(c). $t=2520.1$
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.
$h=1590$ years
(a).$m=150$,
$m(t)=150\times2^{-t/1590},$
(b). $t=1000$,
$m(1000)=150\times2^{1000/1590}=96.998$
(c).$50=150\times2^{-t/1590},$
$0.333=2^{-t/1590}$,
$\log 0.333=\frac{-t}{1590}\log2$,
$t=2520.1$
