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Cambridge IGCSE Maths (0580) · Topic 1: Number · 1.17

Cambridge IGCSE Maths 0580 Exponential Growth and Decay Questions

Exponential Growth and Decay questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise exponential growth and decay →Exponential Growth and Decay notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Exponential Growth and Decay questions: Extended

Extended content, for Papers 2 and 4.

Question 1 Extended calculator · easy

A town has a population of \(24\,000\). The population grows by \(3\%\) each year.
Work out the population after \(5\) years, to the nearest whole number.

Show the worked answer
  1. Multiplier: \(1.03\).
  2. \(24\,000 \times 1.03^5 = 27\,822.5\ldots\)

Answer: \(27\,823\)

Question 2 Extended non-calculator · easy · 2 marks

The mass of a radioactive sample halves every 5 years. The mass is 64 g now. Find the mass after 20 years.

Show the answer and mark scheme
  • M1 64 × (1/2)⁴ or four halvings
  • A1 4 cao

Answer: \(4\) g

Question 3 Extended calculator · medium

A car costs $\(18\,500\). Its value falls by \(12\%\) each year.
Work out its value after \(3\) years. Give your answer to the nearest cent.

Show the worked answer
  1. Multiplier: \(1 - 0.12 = 0.88\).
  2. \(18\,500 \times 0.88^3 = 12\,607.232\)

Answer: $\(12\,607.23\)

Question 4 Extended non-calculator · medium

A population of bacteria doubles every \(20\) minutes. At the start there are \(500\) bacteria.
How many are there after \(2\) hours?

Show the worked answer
  1. \(2\) hours \(= 120\) minutes \(= 6\) lots of \(20\) minutes.
  2. \(500 \times 2^6 = 500 \times 64 = 32\,000\).

Answer: \(32\,000\)

Question 5 Extended calculator · medium

The mass of a radioactive substance falls by \(15\%\) each hour. At the start the mass is \(80\) g.
Work out the mass after \(4\) hours, correct to 3 significant figures.

Show the worked answer
  1. Multiplier: \(0.85\).
  2. \(80 \times 0.85^4 = 41.7605\) g.

Answer: \(41.8\) g

Question 6 Extended non-calculator · medium · 2 marks

Write down the multiplier for

(a) an increase of 7% (b) a decrease of 15%.

Show the answer and mark scheme
  • B1 (a) 1.07
  • B1 (b) 0.85

Answer: (a) \(1.07\) (b) \(0.85\)

Question 7 Extended calculator · hard

$\(5000\) is invested at \(4\%\) per year compound interest.
After how many whole years will it first be worth more than $\(6000\)?

Show the worked answer
  1. After \(n\) years the value is \(5000 \times 1.04^n\).
  2. \(n = 4\): \(5000 \times 1.04^4 = 5849.29\) (not yet).
  3. \(n = 5\): \(5000 \times 1.04^5 = 6083.26\), more than $\(6000\).

Answer: \(5\) years

Question 8 Extended calculator · hard

The value of a painting rises from $\(2000\) to $\(2420\) in \(2\) years. It rises by the same percentage each year.
Find this percentage.

Show the worked answer
  1. \(2000 \times m^2 = 2420\), so \(m^2 = 1.21\) and \(m = 1.1\).
  2. A multiplier of \(1.1\) is an increase of \(10\%\) each year.

Answer: \(10\%\)

Question 9 Extended calculator · hard · 4 marks

Town A has 50 000 people and its population grows by 2% each year. Town B has 42 000 people and its population grows by 5% each year. After how many complete years is the population of Town B first greater than the population of Town A?

Show the answer and mark scheme
  • M1 50 000 × 1.02ⁿ and 42 000 × 1.05ⁿ for the same n
  • M1 compares for n = 6: 56 308 (A) and 56 284 (B)
  • M1 compares for n = 7: 57 434 (A) and 59 098 (B)
  • A1 7

Answer: \(7\) years

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test exponential growth and decay?

Exponential Growth and Decay is Extended content (syllabus 1.17), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more exponential growth and decay questions?

In the 0580 practice for topic 1 (Number), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More number questions