Answer
a. $m(t)=3\times2^{-t/10}$
b. $r=0.0693$
c. $m(60)=0.046875$
d. $t=248.44$ seconds
Work Step by Step
-The formula for radio-active decaying substances is,
$m(t)=m_0e^{-rt}$. Whereas, $m_0$ is the Initial mass, $r$ is the rate of decaying and it is $r=\frac{\ln2}{h}$. or $m(t)=m_02^{-t/h}$. Whereas, $h$ is the half-life.
a. $m(t)=m_02^{-t/h}$, $m_0=3, h=10$
$m(t)=3\times2^{-t/10}$
b. $r=\frac{\ln2}{h}=\frac{\ln2}{10}=0.0693$
c. $m(60)=3\times2{-6}=\frac{3}{64}=0.046875$
d. $10^{-6}=3e^{-00693t}$,
$\frac{1}{10^6\times3}=e^{-00693t}$,
$\ln(\frac{1}{10^6\times3})=-0.0693t$,
$t=248.44$ seconds
