Study Notes
Exponential growth and decay describe how quantities increase or decrease at a consistent percentage rate over time.
- Exponential Growth — when a quantity increases by a fixed percentage each period. Example: A bank account balance growing by 5% interest annually.
- Exponential Decay — when a quantity decreases by a fixed percentage each period. Example: A car's value decreasing by 10% each year.
- Compound Interest Formula — used to calculate exponential growth or decay, with the sign changing for decay. Example: A = P(1 + r)^t for growth, A = P(1 - r)^t for decay.
Exam Tips
Key Definitions to Remember
- Exponential Growth
- Exponential Decay
- Compound Interest Formula
Common Confusions
- Mixing up growth and decay formulas
- Forgetting to adjust the formula for decay by using a minus sign
Typical Exam Questions
- How much will a loan of $18,500 grow to after 2 years at 21% interest? Use the compound interest formula to find the total amount.
- What will be the population in 2020 if it decreases by 0.6% annually from 7.4 million in 2014? Apply the decay formula to calculate the population.
- How long does it take for a colony of bacteria growing at 5% per hour to double? Use the rule of 70 or solve using logarithms.
What Examiners Usually Test
- Ability to apply the compound interest formula for growth and decay
- Understanding of how exponential functions appear on graphs
- Calculating time periods for doubling or halving quantities