a) For a particular radioactive substance, the mass $m$ (in grams) at a time $t$ in years is given by $m = m_0e^{-0.02t}$, where $m_0$ is the original mass. If the original mass is $500$g, find the mass after $10$ years.
b) The half life of any material is the time taken for half of the mass to decay. Find the half-life of this substance.
a) $500e^{-0.02}$ - 490.1
b) $e^{-0.02t} = 0.5$
$\Rightarrow\:$ $-0.02t = \ln(0.5)$
$\Rightarrow\:$ $t = \frac{\ln(0.5)}{-0.02}$
$\Rightarrow\:$ $t = 34.7$
Are my workings correct?
You have the formula
$m = m_0e^{-0.02t}$
and are given the original mass, $m_0$, of $500$g and want to find the mass, $m$, after $t=10$ years.
All you have to do is plug in these values
$m = m_0e^{-0.02t} = 500e^{-0.02 \cdot 10}$
Part $b$ is correct.