Exponential Growth and Decay

Summary and Exam Tips for Exponential Growth and Decay

Exponential Growth and Decay is a subtopic of Number, which falls under the subject Mathematics in the Cambridge IGCSE curriculum. This concept involves understanding how quantities increase or decrease at a constant percentage rate over time. Key learning objectives include:

• Exponential Growth: This occurs when a quantity increases by a consistent percentage over equal time intervals. The formula used is similar to the compound interest formula: $A = P(1 + r)^t$, where $A$ is the amount, $P$ is the initial principal balance, $r$ is the rate of growth, and $t$ is the time.

• Exponential Decay: This is the opposite, where a quantity decreases by a consistent percentage. The formula is $A = P(1 - r)^t$.

• Graphical Representation: Exponential growth functions produce graphs that curve upwards sharply, while decay functions slope downwards.

Applications include financial calculations, such as compound interest and depreciation, as well as modeling population changes and biological growth.

Exam Tips

• Understand the Formula: Be comfortable with the exponential growth and decay formula. Remember, for decay, the rate is subtracted: $A = P(1 - r)^t$.

• Practice with Real-Life Scenarios: Solve problems involving financial growth, population changes, and depreciation to solidify your understanding.

• Graph Interpretation: Be able to interpret and sketch graphs of exponential functions, noting how they rise or fall sharply.

• Check Units and Timeframes: Always ensure that the time period and rate are consistent in your calculations.

• Use Past Papers: Practice with past exam questions to familiarize yourself with the types of problems you might encounter.