11 The height \(h \mathrm {~cm}\) of a sunflower plant \(t\) days after planting the seed is modelled by \(\mathrm { h } = \mathrm { a } + \mathrm { b }\) Int for \(t \geqslant 9\), where \(a\) and \(b\) are constants. The sunflower is 10 cm tall 10 days after planting and 200 cm tall 85 days after planting.
- Show that the value of \(b\) which best models these values is 88.8 correct to \(\mathbf { 3 }\) significant figures.
- Find the corresponding value of \(a\).
- Explain why the model is not suitable for small positive values of \(t\).
- Explain why the model is not suitable for very large positive values of \(t\).
- Show that the model indicates that the sunflower grows to 1 m in height in less than half the time it takes to grow to 2 m .
- Find the value of \(t\) for which the rate of growth is 3 cm per day.