| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Logistic growth model |
| Difficulty | Standard +0.8 This logistic growth question requires multiple algebraic manipulations including exponential equations, logarithms, and limit analysis. While part (a) is routine substitution, parts (b-d) demand understanding of exponential manipulation, solving transcendental equations, and proving a population bound through algebraic rearrangement and limit behavior—significantly more sophisticated than standard C3 exponential questions. |
| Spec | 1.06g Equations with exponentials: solve a^x = b1.06i Exponential growth/decay: in modelling context |
7. A particular species of orchid is being studied. The population $p$ at time $t$ years after the study started is assumed to be
$$p = \frac { 2800 a \mathrm { e } ^ { 0.2 t } } { 1 + a \mathrm { e } ^ { 0.2 t } } , \text { where } a \text { is a constant. }$$
Given that there were 300 orchids when the study started,
\begin{enumerate}[label=(\alph*)]
\item show that $a = 0.12$,
\item use the equation with $a = 0.12$ to predict the number of years before the population of orchids reaches 1850 .
\item Show that $p = \frac { 336 } { 0.12 + \mathrm { e } ^ { - 0.2 t } }$.
\item Hence show that the population cannot exceed 2800.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q7 [11]}}