| Exam Board | Edexcel |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2020 |
| Session | October |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Exponential growth/decay - direct proportionality (dN/dt = kN) |
| Difficulty | Easy -1.2 This is a direct recall question asking students to translate a standard exponential growth statement ('rate proportional to amount') into the differential equation dn/dt = kn or its solution n = Ae^(kt). It requires only recognition of a textbook model with no problem-solving, integration, or application of initial conditions. |
| Spec | 1.07t Construct differential equations: in context |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Any equation involving an exponential of correct form | M1 | E.g. \(n = e^{\pm t}\), \(n = Ae^{\pm t}\), \(n = Ae^{\pm kt}\); condone \(n = A + Be^{\pm t}\) |
| \(n = Ae^{kt}\) (where \(A\) and \(k\) are positive constants) | A1 | Two constants must be different; also allow \(n = Ak^t\) |
## Question 8:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Any equation involving an exponential of correct form | M1 | E.g. $n = e^{\pm t}$, $n = Ae^{\pm t}$, $n = Ae^{\pm kt}$; condone $n = A + Be^{\pm t}$ |
| $n = Ae^{kt}$ (where $A$ and $k$ are positive constants) | A1 | Two constants must be different; also allow $n = Ak^t$ |
---\begin{enumerate}
\item A new smartphone was released by a company.
\end{enumerate}
The company monitored the total number of phones sold, $n$, at time $t$ days after the phone was released.
The company observed that, during this time,\\
the rate of increase of $n$ was proportional to $n$\\
Use this information to write down a suitable equation for $n$ in terms of $t$.\\
(You do not need to evaluate any unknown constants in your equation.)
\hfill \mbox{\textit{Edexcel Paper 1 2020 Q8 [2]}}