| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | Exponential Functions |
| Type | Linear transformation to find constants |
| Difficulty | Moderate -0.8 This is a straightforward exponential/logarithm question requiring routine manipulation: substitute t=2 into the log equation, then convert log form to exponential form by comparing coefficients. The interpretation in part (c) is standard. All steps are textbook exercises with no problem-solving insight needed. |
| Spec | 1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form1.06i Exponential growth/decay: in modelling context |
16. An area of sea floor is being monitored.
The area of the sea floor, $S \mathrm {~km} ^ { 2 }$, covered by coral reefs is modelled by the equation
$$S = p q ^ { t }$$
where $p$ and $q$ are constants and $t$ is the number of years after monitoring began.\\
Given that
$$\log _ { 10 } S = 4.5 - 0.006 t$$
\begin{enumerate}[label=(\alph*)]
\item find, according to the model, the area of sea floor covered by coral reefs when $t = 2$
\item find a complete equation for the model in the form
$$S = p q ^ { t }$$
giving the value of $p$ and the value of $q$ each to 3 significant figures.
\item With reference to the model, interpret the value of the constant $q$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q16 [6]}}