| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 6 |
| Topic | Exponential Equations & Modelling |
| Type | Finding x from given y value |
| Difficulty | Moderate -0.8 This is a straightforward exponential decay question requiring only standard techniques: finding the decay constant from two given values, then applying the exponential model to find missing values and solve for time. The calculations are routine with no conceptual challenges or novel problem-solving required, making it easier than average but not trivial since it involves logarithms and multi-step application. |
| Spec | 1.06i Exponential growth/decay: in modelling context |
| \(t\) | 0 | 5 | 10 | 25 |
| \(m\) | 200 | 160 |
The mass of a substance is decreasing exponentially. Its mass is $m$ grams at time $t$ years. The following table shows certain values of $t$ and $m$.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
$t$ & 0 & 5 & 10 & 25 \\
\hline
$m$ & 200 & 160 & & \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Find the values missing from the table. [2]
\item Determine the value of $t$, correct to the nearest integer, for which the mass is 50 grams. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2024 Q6 [6]}}