Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Exponential Growth and Decay — compound change, depreciation and population models — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Exponential Growth and Decay in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Exponential Growth and Decay revision-guide angle, while Tutopiya’s Exponential Growth and Decay subtopic page owns the learning resource and the free Exponential Growth and Decay quiz owns the practice.

Exponential Growth and Decay sits in the Number unit of Cambridge IGCSE Mathematics (0580/0607) and tests whether you can model repeated proportional change — population growth, radioactive decay, depreciation of assets. The formula looks intimidating until you recognise it as compound interest in disguise. This guide explains what the subtopic covers, how to set up and solve real exam questions, and where to practise each skill.

Key takeaways

• Exponential growth uses multiplier (1 + r)ⁿ; decay uses (1 − r)ⁿ where r is the rate as a decimal.
• The standard formula is V = V₀ × kⁿ, where k is the growth/decay factor per period and n is the number of periods.
• Depreciation, population change and cooling problems all share the same structure — identify V₀, k and n first.
• This subtopic builds on Earnings, Simple and Compound Interest and Exponents and Surds.

What is Exponential Growth and Decay in Cambridge IGCSE Maths?

Exponential growth and decay describes quantities that change by a fixed percentage each time period, not by a fixed amount. A population growing 3% per year, or a car losing 15% of its value each year, follows an exponential model. In Cambridge IGCSE Mathematics, you calculate future or past values, find the number of periods, or determine the rate — always using the compound-change formula. It appears in both calculator and structured questions.

Read the full explanation, worked examples and notes on Tutopiya’s Exponential Growth and Decay subtopic page before you attempt questions.

The core formula and what each part means

Symbol	Meaning	Example
V₀	Initial value (starting amount)	$12 000 car value
k	Multiplier per period	Growth 4% → k = 1.04; decay 10% → k = 0.90
n	Number of time periods	5 years
V	Final value after n periods	V = V₀ × kⁿ

How to solve exponential growth and decay — step by step

1. Identify the type — growth (increasing) or decay (decreasing).
2. Write V₀ — the starting value from the question.
3. Find k — convert the percentage rate to a decimal, then k = 1 + r (growth) or k = 1 − r (decay).
4. Count n — how many complete periods have passed.
5. Substitute into V = V₀ × kⁿ and evaluate. On calculator papers, use the power key carefully.

Test yourself with the free Exponential Growth and Decay quiz once the setup steps feel automatic.

Growth vs decay: how to tell from the question

Signal in the question	Type	Multiplier k
”increases by …%”, “grows”, “population rises”	Growth	1 + r
”decreases by …%”, “depreciates”, “decays”, “loses value”	Decay	1 − r
Half-life / radioactive	Decay	k = ½ per half-life

Exponential Growth and Decay in past-paper wording: command words that matter

Command word / phrase	What the question wants	Typical stem
Calculate / Work out	Find V, n, or k using the formula	”Work out the value after 6 years.”
Find the value of n	Number of periods (may need trial or logs on calculator)	“After how many years will the population exceed 50 000?”
Write down an expression	Formula with letters, not evaluated	”Write an expression for the value after t years.”
Show that	Prove a given result with substitution	”Show that the value after 3 years is $9 720.”
Describe the effect	Explain growth or decay in context	”Describe what happens to the mass over time.”

Worked exam-style stems (how to answer the wording)

1. “A car costs $20 000. Its value depreciates by 12% per year. Work out its value after 4 years.” V₀ = 20 000, k = 0.88, n = 4 → V = 20 000 × 0.88⁴ = $11 993.63 (to nearest cent). Reward: correct multiplier 0.88, not 0.12; correct power 4.
2. “The population of a town is 45 000. It increases by 2.5% each year. Write an expression for the population after t years.” Answer: 45 000 × 1.025ᵗ. Reward: correct base and exponent variable; no premature evaluation.
3. “A substance has mass 800 g. It decays by 5% per hour. Show that after 10 hours the mass is approximately 477 g.” V = 800 × 0.95¹⁰ ≈ 477. Reward: method with 0.95¹⁰ shown; answer matching to required accuracy.

Work the full set on the Number topical past-paper questions and the Exponential Growth and Decay quiz to lock the method in.

How Exponential Growth and Decay connects to the rest of Number

Compound interest from Earnings, Simple and Compound Interest uses the same V = V₀ × kⁿ structure. Index laws from Exponents and Surds help when simplifying powers. Use the Cambridge IGCSE Maths resource hub to move between related subtopics.

Common mistakes students make

• Using r instead of k — a 8% decay rate means k = 0.92, not 0.08 or 8.
• Treating exponential change as linear (subtracting a fixed amount each year for depreciation).
• Confusing n (number of periods) with the rate percentage.
• Rounding k too early, which distorts the final answer on longer time periods.

When you need more support

If setup or interpretation keeps going wrong, work through the Compound Interest quiz and the Number topical past-paper questions, then get focused help from a Cambridge IGCSE Maths tutor.

Frequently asked questions

What is the difference between simple and compound change? Simple change adds or subtracts a fixed amount each period. Exponential (compound) change applies the rate to the current value each time, so the change itself grows or shrinks.

Do I need logarithms for Exponential Growth and Decay? Most IGCSE questions let you find n by trial on a calculator or give n directly. Extended papers may require log work — check your syllabus tier.

Is depreciation growth or decay? Decay — the value decreases each period, so k < 1.

How do I revise Exponential Growth and Decay effectively? Master the V = V₀ × kⁿ setup, practise labelling growth vs decay, then take the Exponential Growth and Decay quiz. Revisit any word problems where you misidentified k.

Ready to master Cambridge IGCSE Maths Exponential Growth and Decay?

Start with the Exponential Growth and Decay subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist to turn this subtopic into guaranteed marks.

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