This study notes covers Worked Examples 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 5 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 8
Practice
12 questions
Recall
22 flashcards
Worked Examples
Example 1: Bacteria Growth
Problem: A bacteria culture starts with 500 bacteria and doubles every 3 hours. How many bacteria are there after 12 hours?
Solution:
Step 1: This is growth (doubling)
Step 2: Number of doubling periods = 12 ÷ 3 = 4
Step 3: Use doubling formula: N = N₀ × 2ⁿ
Step 4: N = 500 × 2⁴ = 500 × 16 = 8000
Answer: 8000 bacteria
Example 2: Car Depreciation
Problem: A car worth £15,000 depreciates by 18% each year. What is its value after 4 years?
Solution:
Step 1: This is decay (depreciating)
Step 2: 18% = 0.18
Step 3: Multiplier = 1 - 0.18 = 0.82
Step 4: N = 15000 × (0.82)⁴
Step 5: N = 15000 × 0.452 = £6,780
Answer: £6,780
Example 3: Radioactive Half-life
Problem: A radioactive sample has 800g initially and a half-life of 6 years. How much remains after 18 years?
Solution:
Step 1: This is decay with half-life
Step 2: Number of half-life periods = 18 ÷ 6 = 3
Step 3: Use half-life formula: N = N₀ × (0.5)ⁿ
Step 4: N = 800 × (0.5)³ = 800 × 0.125 = 100g
Answer: 100g
Example 4: Compound Interest Investment
Problem: £2000 is invested at 6% compound interest per year. What is the value after 5 years?
Solution:
Step 1: This is growth (compound interest)
Step 2: 6% = 0.06
Step 3: Multiplier = 1 + 0.06 = 1.06
Step 4: N = 2000 × (1.06)⁵
Step 5: N = 2000 × 1.338 = £2,676
Answer: £2,676