| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 7 |
| Topic | Exponential Equations & Modelling |
| Type | ln(y) vs ln(x) linear graph |
| Difficulty | Standard +0.3 This is a straightforward logarithmic modeling question requiring students to convert between exponential and linear forms (finding p from y-intercept and q from gradient), substitute values to test the model, and interpret a constant. All steps are routine A-level techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form2.02c Scatter diagrams and regression lines |
\includegraphics{figure_2}
The resting heart rate, $h$, of a mammal, measured in beats per minute, is modelled by the equation
$$h = pm^q$$
where $p$ and $q$ are constants and $m$ is the mass of the mammal measured in kg.
Figure 2 illustrates the linear relationship between $\log_{10} h$ and $\log_{10} m$
The line meets the vertical $\log_{10} h$ axis at 2.25 and has a gradient of $-0.235$
\begin{enumerate}[label=(\alph*)]
\item Find, to 3 significant figures, the value of $p$ and the value of $q$. [3]
\end{enumerate}
A particular mammal has a mass of 5kg and a resting heart rate of 119 beats per minute.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Comment on the suitability of the model for this mammal. [3]
\item With reference to the model, interpret the value of the constant $p$. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q8 [7]}}