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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?

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  • $\begingroup$ $(b)$ seems to be ok, but part (a) is not ok. Review and correct. $\endgroup$ Commented May 2, 2016 at 20:25

1 Answer 1

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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.

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