15.
The resting metabolic rate, \(R \mathrm { ml }\) of oxygen consumed per hour, of a particular species of mammal is modelled by the formula,
$$R = a M ^ { b }$$
where
- \(M\) grams is the mass of the mammal
- \(\quad a\) and \(b\) are constants
- Show that this relationship can be written in the form
$$\log _ { 10 } R = b \log _ { 10 } M + \log _ { 10 } a$$
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f953fd1c-447f-4e97-a42a-5264c053fda0-30_700_901_1005_667}
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\caption{Figure 3}
\end{figure}
A student gathers data for \(R\) and \(M\) and plots a graph of \(\log _ { 10 } R\) against \(\log _ { 10 } M\)
The graph is a straight line passing through points \(( 0.7,1.2 )\) and \(( 1.8,1.9 )\) as shown in Figure 3.
Using this information, find a complete equation for the model.
Write your answer in the form
$$R = a M ^ { b }$$
giving the value of each of \(a\) and \(b\) to 3 significant figures.With reference to the model, interpret the value of the constant \(a\)