Growth and decay
Exponential change: A = P(1+r)t for growth; P(1-r)t for decay.
Compound interest, depreciation, population growth, radioactive decay all use the same formula. The ratio (1+r) or (1-r) is applied repeatedly.
Worked examples
£1000 at 5% pa for 4 years: 1000 × 1.054 ≈ £1215.51.
Car £20,000 depreciating 12% pa for 3 years: 20,000 × 0.883 ≈ £13,629.44.
Population 5000, growing 3% pa, after 10 years: 5000 × 1.0310 ≈ 6720.
Frequently asked questions
Continuous compounding?
A-Level only. GCSE uses discrete annual (or monthly) compounding.
Half-life?
Time for amount to halve. Solve P/2 = P×decayt; e.g. for 0.95t = 0.5 ⇒ t ≈ 13.5.