GCSE & IGCSE maths practice

Exponential growth and decay questions and answers

In exponential growth or decay, an amount is multiplied by the same number each time period: value $= \text{start} \times \text{multiplier}^n$ . Growth multipliers are above 1 (3% growth: 1.03); decay multipliers are between 0 and 1 (20% decay: 0.8).

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Exponential growth and decay: lesson Compound interest calculator

Where exponential growth and decay comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: set up, solve and interpret growth and decay problems. Higher: recognise and interpret exponential graphs.
Cambridge IGCSE (0580)	Extended only: use exponential growth and decay in relation to population and finance.

The method

Find the multiplier for one time period.
Value after n periods = start × multiplierⁿ.
Doubling: multiplier 2; halving: 0.5.
To find when a target is reached, try values of n.

Exponential growth and decay questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

50 bacteria double every hour. How many are there after 4 hours?

Question 2Warm-upFoundation

A population of 2000 grows by 3% a year. What is it after 1 year?

Exam-style

Question 3Exam-styleFoundation

A machine worth £8000 loses 20% of its value each year. What is it worth after 2 years?

Question 4Exam-styleFoundation

A ball is dropped from 5 m. Each bounce reaches 60% of the previous height. How high does it go after the 3rd bounce?

Question 5Exam-styleFoundation

A population is modelled by $N = 500 \times 1.04^t$ , where $t$ is in years. Find $N$ when $t = 3$ , to the nearest whole number.

Question 6Exam-styleFoundation

What is the multiplier for a decrease of 2.5% per year?

Challenge

Question 7ChallengeFoundation

£1000 grows at 8% a year. After how many whole years has it first doubled?

years

Question 8ChallengeFoundation

An insect population of 6000 falls by a third each week. How many are there after 3 weeks, to the nearest whole number?

Common mistakes

Adding the same amount each time (that's linear growth).
Using 0.2 instead of 0.8 for a 20% decrease.
Rounding during the calculation.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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