4 The height \(h\) metres of a tree after \(t\) years is modelled by the equation
$$h = a - b \mathrm { e } ^ { - k t }$$
where \(a\), \(b\) and \(k\) are positive constants.
- Given that the long-term height of the tree is 10.5 metres, and the initial height is 0.5 metres, find the values of \(a\) and \(b\).
- Given also that the tree grows to a height of 6 metres in 8 years, find the value of \(k\), giving your answer correct to 2 decimal places.