| Type | Formula | Variables | When to Use |
|---|---|---|---|
| Exponential Growth | N = N₀ × (1 + r)ⁿ | N₀ = initial, r = rate, n = time periods | Population, compound interest, bacteria |
| Exponential Decay | N = N₀ × (1 - r)ⁿ | N₀ = initial, r = rate, n = time periods | Radioactivity, depreciation, medicine |
| Half-life | N = N₀ × (0.5)ⁿ | n = number of half-life periods | Radioactive decay, drug elimination |
| Doubling Time | N = N₀ × 2ⁿ | n = number of doubling periods | Bacterial growth, compound interest |
This key facts covers Essential Growth & Decay Formulas 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 2 of 9 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
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
What is the formula for exponential decay?
N = N₀ × (1 - r)ⁿ
Where:
N = final amount
N₀ = initial amount
r = decay rate (as decimal)
n = number of time periods
What is the formula for half-life decay?
N = N₀ × (0.5)ⁿ
Where:
N = remaining amount
N₀ = initial amount
n = number of half-life periods