| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential growth/decay model setup |
| Difficulty | Moderate -0.8 This is a straightforward exponential decay question requiring only direct substitution (part a), solving a simple exponential equation using logarithms (part b), substitution again (part c), and sketching a standard decay curve (part d). All parts are routine applications of standard techniques with no problem-solving insight required, making it easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1000\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1000e^{-5730c} = 500\) | M1 | |
| \(e^{-5730c} = \frac{1}{2}\) | A1 | |
| \(-5730c = \ln\frac{1}{2}\) | M1 | |
| \(c = 0.000121\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(R = 1000e^{-22920c} = 62.5\) | M1 A1 | Accept 62–63 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Correct decreasing exponential shape | B1 | |
| \(R\)-intercept at \(1000\) labelled | B1 |
# Question 5:
## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1000$ | B1 | |
## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1000e^{-5730c} = 500$ | M1 | |
| $e^{-5730c} = \frac{1}{2}$ | A1 | |
| $-5730c = \ln\frac{1}{2}$ | M1 | |
| $c = 0.000121$ | A1 | cao |
## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $R = 1000e^{-22920c} = 62.5$ | M1 A1 | Accept 62–63 |
## Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct decreasing exponential shape | B1 | |
| $R$-intercept at $1000$ labelled | B1 | |
---5. The radioactive decay of a substance is given by
$$R = 1000 \mathrm { e } ^ { - c t } , \quad t \geqslant 0 .$$
where $R$ is the number of atoms at time $t$ years and $c$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Find the number of atoms when the substance started to decay.
It takes 5730 years for half of the substance to decay.
\item Find the value of $c$ to 3 significant figures.
\item Calculate the number of atoms that will be left when $t = 22920$.
\item In the space provided on page 13, sketch the graph of $R$ against $t$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 2008 Q5 [9]}}