| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Compound interest and percentage growth |
| Difficulty | Moderate -0.8 This is a straightforward C2 exponential growth question with three routine parts: sketching y=a^x (standard shape), direct substitution into the formula, and solving a^x=2 using logarithms. All parts follow textbook procedures with no problem-solving insight required, making it easier than average but not trivial due to the logarithm manipulation in part (c). |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b1.06i Exponential growth/decay: in modelling context |
Every £1 of money invested in a savings scheme continuously gains interest at a rate of 4% per year. Hence, after $x$ years, the total value of an initial £1 investment is £$y$, where
$$y = 1.04^x.$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = 1.04^x$, $x \geq 0$. [2]
\item Calculate, to the nearest £, the total value of an initial £800 investment after 10 years. [2]
\item Use logarithms to find the number of years it takes to double the total value of any initial investment. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [7]}}