Knowledge Organiser: Exponential Growth and Decay
Part of Growth & Decay · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Exponential Growth and Decay within Growth & Decay for GCSE Mathematics. Revise Growth & Decay in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 9 of 9 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 9 of 9
Practice
12 questions
Recall
22 flashcards
Knowledge Organiser: Exponential Growth and Decay
Key Terms
- Exponential growth: Quantity increases by a fixed percentage each period
- Exponential decay: Quantity decreases by a fixed percentage each period
- Multiplier: Growth uses (1 + r); decay uses (1 − r), where r is the decimal rate
- Half-life: Time taken for a quantity to halve (decay to 50%)
- Compound interest: Interest calculated on the accumulated amount each period
- N₀: The initial (starting) amount
Must-Know Facts
- Growth multiplier for r%: (1 + r/100); decay multiplier: (1 − r/100)
- 5% growth over 4 years ≠ 20% total (it is 21.6% — compound, not linear)
- Doubling every period: N = N₀ × 2ⁿ
- Half-life: N = N₀ × (0.5)ⁿ where n = time ÷ half-life period
- n is the number of TIME PERIODS, not the total time
- Growth gives J-shaped curve; decay gives reverse J-shaped curve
Key Formulas
- Exponential growth: N = N₀ × (1 + r)ⁿ
- Exponential decay: N = N₀ × (1 − r)ⁿ
- Doubling: N = N₀ × 2ⁿ
- Half-life: N = N₀ × (0.5)ⁿ
- Compound interest: A = P × (1 + r)ⁿ
- r = rate as a decimal (e.g. 5% → r = 0.05)
Common Mistakes
- Rate as percentage not decimal: Use r = 0.05 for 5%, NOT r = 5 in the formula
- Multiplier for decay: 10% decay uses multiplier 0.9, not 1.1 or 0.1
- Simple vs compound: Simple growth adds the same amount each time; exponential multiplies — don't confuse them
- n is number of periods: n = number of years/periods, NOT the final year number
- Rounding too early: Keep full calculator value until the final step to avoid rounding errors
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Practice Questions for Growth & Decay
A quantity increases by 8% each year. Which multiplier should be used for each year?
Explain the difference between simple interest and compound interest.
Quick Recall Flashcards
12 questions on Growth & Decay — practise free
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