1. A tree was planted.

Exactly 3 years after it was planted, the height of the tree was 2 m . Exactly 5 years after it was planted, the height of the tree was 2.4 m . Given that the height, \(H\) metres, of the tree, \(t\) years after it was planted, can be modelled by the equation $$H ^ { 3 } = p t ^ { 2 } + q$$ where \(p\) and \(q\) are constants,

1. find, to 3 significant figures where necessary, the value of \(p\) and the value of \(q\). Exactly \(T\) years after the tree was planted, its height was 5 m .
2. Find the value of \(T\) according to the model, giving your answer to one decimal place.