- The height, \(h\) metres, of a tree, \(t\) years after being planted, is modelled by the equation
$$h ^ { 2 } = a t + b \quad 0 \leqslant t < 25$$
where \(a\) and \(b\) are constants.
Given that
- the height of the tree was 2.60 m , exactly 2 years after being planted
- the height of the tree was 5.10 m , exactly 10 years after being planted
- find a complete equation for the model, giving the values of \(a\) and \(b\) to 3 significant figures.
Given that the height of the tree was 7 m , exactly 20 years after being planted
evaluate the model, giving reasons for your answer.