Long-term behaviour and limits

A question is this type if and only if it requires identifying the long-term limit or asymptotic behaviour of an exponential model as t approaches infinity.

1 questions · Moderate -0.8

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Edexcel AS Paper 1 2023 June Q11
6 marks Moderate -0.8
  1. 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,
  1. find the height of the plant when it was first measured,
  2. 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.
  3. Deduce the value of this limit.