| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Exponential growth/decay - direct proportionality (dN/dt = kN) |
| Difficulty | Moderate -0.8 This is a standard textbook exponential decay question requiring only routine application of well-practiced techniques: forming dN/dt = -kN, separating variables, applying initial conditions, and substituting values. All steps are algorithmic with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form1.08k Separable differential equations: dy/dx = f(x)g(y) |
I don't see any extracted mark scheme content in your message. You've provided instructions for how to clean up content, but the actual mark scheme text for Question 6 appears to be incomplete or missing.
Please provide the full mark scheme content that needs to be cleaned up, and I'll format it according to your specifications.6. A radioactive isotope decays in such a way that the rate of change of the number $N$ of radioactive atoms present after $t$ days, is proportional to $N$.
\begin{enumerate}[label=(\alph*)]
\item Write down a differential equation relating $N$ and $t$.
\item Show that the general solution may be written as $N = A \mathrm { e } ^ { - k t }$, where $A$ and $k$ are positive constants.
Initially the number of radioactive atoms present is $7 \times 10 ^ { 18 }$ and 8 days later the number present is $3 \times 10 ^ { 17 }$.
\item Find the value of $k$.
\item Find the number of radioactive atoms present after a further 8 days.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q6 [12]}}