7 The mass, \(M \mathrm {~kg}\), of a species of tree can be modelled by the equation
$$\log _ { 10 } M = 1.93 \log _ { 10 } r + 0.684$$
where \(r \mathrm {~cm}\) is the base radius of the tree.
The base radius of a particular tree of this species is 45 cm .
According to the model,
- find the mass of this tree, giving your answer to 2 significant figures.
- Show that the equation of the model can be written in the form
$$M = p r ^ { q }$$
giving the values of the constants \(p\) and \(q\) to 3 significant figures.
- With reference to the model, interpret the value of the constant \(p\).
Q