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If the rate of decay of a radioactive substance is proportional to its mass $m$ at time $t$, the differential equation is:
A$dm/dt = +km$
B$dm/dt = -km$ (with $k > 0$)
C$dm/dt = k/m$
D$dm/dt = m^2$
Answer & Solution
Correct answer: B. $dm/dt = -km$ (with $k > 0$)
Decay ⇒ $dm/dt$ is negative and proportional to $m$. So $dm/dt = -km$, $k > 0$. Solution: $m(t) = m_0 e^{-kt}$ — exponential decay.
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