Growth and decay problems model real situations like compound interest, population growth, and depreciation. The multiplier method makes these calculations efficient.
Core Formula
where = number of time periods.
Growth Multiplier
Increase of : multiplier = .
5% growth → multiplier = 1.05.
Decay Multiplier
Decrease of : multiplier = .
12% depreciation → multiplier = 0.88.
Worked Example: Compound Interest
Problem
£5000 invested at 3% per year for 4 years.
Solution
Worked Example: Depreciation
Problem
Car worth £20,000 depreciates by 15% per year. Value after 3 years:
Solution
Worked Example: Population
Problem
Population 50,000 grows by 2.5% annually. After 10 years:
Solution
Practice Problems
- £3000 at 4% compound interest for 5 years.
- A laptop worth £800 depreciates by 20% per year. Value after 2 years?
- Bacteria double every hour. Starting with 100, how many after 6 hours?
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Key Takeaways
Growth: multiplier > 1. Decay: multiplier < 1.
Formula: Initial × multiplier^n.
Compound interest means interest earns interest.