| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 8 |
| Topic | Exponential Functions |
| Type | Exponential model with shifted asymptote |
| Difficulty | Moderate -0.8 This is a straightforward exponential decay question requiring only basic substitution (t=0 for initial mass, tââ for long-term behaviour), simple logarithm manipulation to solve for t, and sketching a standard exponential decay curve approaching a horizontal asymptote. All parts are routine applications of standard techniques with no problem-solving insight required, making it easier than average but not trivial since it does require understanding of exponential functions and limits. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context |
In a chemical reaction, the mass $m$ grams of a chemical after $t$ minutes is modelled by the equation
$$m = 20 + 30e^{-0.1t}.$$
\begin{enumerate}[label=(\roman*)]
\item Find the initial mass of the chemical.
What is the mass of chemical in the long term? [3]
\item Find the time when the mass is 30 grams. [3]
\item Sketch the graph of $m$ against $t$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2024 Q6 [8]}}