What is important to know about Growth & decay?

Exponential growth: y = a × bⁿ where b > 1.

What is important to know about Growth & decay?

Exponential decay: y = a × bⁿ where 0 < b < 1.

What is important to know about Growth & decay?

Population growth, bacterial growth and radioactive decay all follow exponential patterns.

⚖️

Ratio & Proportion · Higher

Growth & decay

Q: What is important to know about Growth & decay?

Population growth, bacterial growth and radioactive decay all follow exponential patterns.

Q: What are common mistakes with Growth & decay?

Subtracting 20% four times separately instead of using the multiplier to the power of 4.

Q: What are common mistakes with Growth & decay?

Using an additive model (adding a fixed amount) instead of a multiplicative one.

Q: What exam tips are there for Growth & decay?

Identify: initial value (a), multiplier (b), and number of time periods (n) before substituting.

Q: What exam tips are there for Growth & decay?

Growth and decay questions follow the exact same pattern as compound interest — use the same approach.

Exponential growth and decay describe situations where a quantity increases or decreases by a fixed percentage repeatedly. The same multiplier formula applies as in compound interest.

Revising growth & decay the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Growth & decay GCSE” on the site for the complete guide.

🔑

Key facts to remember

1Exponential growth: y = a × bⁿ where b > 1.
2Exponential decay: y = a × bⁿ where 0 < b < 1.
3Population growth, bacterial growth and radioactive decay all follow exponential patterns.
4The multiplier b = 1 + r/100 (growth) or 1 − r/100 (decay).
5Growth and decay are the same mathematically as compound interest and depreciation.

📐

Formulas

Growth/decay

y = a × bⁿ

a = initial amount, b = multiplier, n = time periods

✍️

Worked examples

Example 1

A population of bacteria doubles every 3 hours. Starting at 500, how many are there after 12 hours?

Working

Number of 3-hour periods = 12 ÷ 3 = 4
Multiplier = 2 (doubling)
Population = 500 × 2⁴ = 500 × 16 = 8000

Answer8000

Example 2

A radioactive substance decays at 20% per year. Starting mass is 400 g. Find the mass after 4 years.

Working

Multiplier = 1 − 0.20 = 0.80
Mass = 400 × 0.8⁴ = 400 × 0.4096 = 163.84 g

Answer163.84 g

⚠️

Common mistakes

✗Subtracting 20% four times separately instead of using the multiplier to the power of 4.

✗Using an additive model (adding a fixed amount) instead of a multiplicative one.

✗Not identifying the number of time periods n correctly.

🎯

Exam tips

✓Identify: initial value (a), multiplier (b), and number of time periods (n) before substituting.

✓Growth and decay questions follow the exact same pattern as compound interest — use the same approach.

Ready to test yourself on Growth & decay?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →

← All topics Dashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶exponential growth decay GCSE Higher maths ▶growth decay GCSE Higher ▶population growth GCSE maths ▶exponential decay GCSE Higher

Opens YouTube — pick any free GCSE video.