| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 9 |
| Topic | Differential equations |
| Type | Exponential growth/decay - direct proportionality (dN/dt = kN) |
| Difficulty | Moderate -0.3 This is a standard exponential decay application requiring setup of dV/dt = -kV, finding k from initial conditions, solving the differential equation, and substituting to find time. Part (b) and (c) require basic modeling awareness. Slightly easier than average due to straightforward setup and routine integration, though multi-part structure provides some substance. |
| Spec | 1.06i Exponential growth/decay: in modelling context1.08k Separable differential equations: dy/dx = f(x)g(y) |
7 As a spherical snowball melts its volume decreases. The rate of decrease of the volume of the snowball at any given time is modelled as being proportional to its volume at that time. Initially the volume of the snowball is $500 \mathrm {~cm} ^ { 3 }$ and the rate of decrease of its volume is $20 \mathrm {~cm} ^ { 3 }$ per hour.
\begin{enumerate}[label=(\alph*)]
\item Find the time that this model would predict for the snowball's volume to decrease to $250 \mathrm {~cm} ^ { 3 }$.
\item Write down one assumption made when using this model.
\item Comment on how realistic this model would be in the long term.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q7 [9]}}