- The height, \(h\) metres, of a plant, \(t\) years after it was first measured, is modelled by the equation
$$h = 2.3 - 1.7 \mathrm { e } ^ { - 0.2 t } \quad t \in \mathbb { R } \quad t \geqslant 0$$
Using the model,
- find the height of the plant when it was first measured,
- show that, exactly 4 years after it was first measured, the plant was growing at approximately 15.3 cm per year.
According to the model, there is a limit to the height to which this plant can grow.
- Deduce the value of this limit.