Easy -1.2 This is a straightforward recall question asking students to write down the standard differential equation for exponential decay (dN/dt = -kN). It requires only knowledge of the definition that 'rate proportional to amount' translates to this form, with no solving or manipulation needed.
11. In a science experiment, a radio active particle, \(N\), decays over time, \(t\), measured in minutes. The rate of decay of a particle is proportional to the number of particles remaining.
Write down a suitable equation for the rate of change of the number of particles, \(N\) in terms of \(t\).
Write down a suitable equation for the rate of change of the number of particles, \(N\) in terms of \(t\)
Answer
Marks
M1
Any equation of the correct form, involving \(N\) and an exponential in \(t\). e.g. \(N = e^{\pm t}\), \(N = Ae^{\pm t}\), \(N = Ae^{\pm kt}\) or allow \(\ln N = kt + c\)
A1
\(N = Ae^{-kt}\)
(2) marks total for Question 11
Write down a suitable equation for the rate of change of the number of particles, $N$ in terms of $t$
| | M1 | Any equation of the correct form, involving $N$ and an exponential in $t$. e.g. $N = e^{\pm t}$, $N = Ae^{\pm t}$, $N = Ae^{\pm kt}$ or allow $\ln N = kt + c$ |
| --- | --- | --- |
| | A1 | $N = Ae^{-kt}$ |
**(2) marks total for Question 11**
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11. In a science experiment, a radio active particle, $N$, decays over time, $t$, measured in minutes. The rate of decay of a particle is proportional to the number of particles remaining.
Write down a suitable equation for the rate of change of the number of particles, $N$ in terms of $t$.\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q11 [2]}}