Quadratic model from data points

A question is this type if and only if it asks to find constants in a non-linear model (H³ = pt² + q or similar) given data points.

1 questions · Moderate -0.8

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Edexcel P1 2021 January Q2
6 marks Moderate -0.8
  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.