Growth and Decay

Growth and decay extend the compound interest and depreciation concepts into broader contexts. This topic is particularly important for Higher tier students in the Edexcel GCSE Mathematics (1MA1) specification, though Foundation students also encounter simpler versions. Questions involve exponential models, multipliers and interpreting growth/decay in real-world settings.

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Key Vocabulary

Term	Meaning
Exponential growth	A quantity increases by a fixed percentage each time period
Exponential decay	A quantity decreases by a fixed percentage each time period
Multiplier	The factor applied each time period (>1 for growth, between 0 and 1 for decay)
Half-life	The time taken for a quantity to reduce to half its original value
Model	A mathematical equation that represents a real-world situation

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Exponential Growth

When a quantity grows by a fixed percentage each period, we use the formula:

A = P x k^n

where:

• A = final amount
• P = initial amount
• k = multiplier (k > 1 for growth)
• n = number of time periods