Sequences

Growth and Decay

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The Link Between Sequences and Growth / Decay
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Arithmetic sequences can be used to model a situation of linear growth due to their constant addition (or subtraction) of a certain value.


Conversely, geometric sequences can be used to model situations of exponential growth due to their repeated multiplication by a certain value.


  • GPs represent exponential growth where r > 1; and

  • Represent exponential decay where 0 < r < 1.

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Example
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James starts a new job manufacturing pieces of furniture. Due to the training process of the job, for the first four weeks, his output increases each day. 


On his first day, he manufactures 10 pieces of furniture, with this number increasing by 2 pieces each day, including the last day of the fourth week.


1. Create a recursive rule that expresses the number of furniture items completed on each day of the first four weeks.


Tₙ₊₁ = Tₙ + 2, T₁ = 10


2. How many pieces of furniture does he complete on the last day of the fourth week (day 28)?


T₂₈ = 10 + (27)2 = 64






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