Understanding Compound Growth and Decay

What is Compound Growth?

Compound growth, also known as exponential growth, is where an amount increases by a fixed percent each time period.
An example of compound growth is interest in a bank account that is compounded yearly, monthly, weekly, or even daily.
The formula for compound growth is: A = P(1 + r/n)^(nt), where A represents the final amount, P is the principal amount, r is the annual interest rate (in decimal form), n is the amount of times that interest is compounded per unit t, and t is the time the money is invested for.

What is Compound Decay?

Compound decay, also known as exponential decay, is where an amount decreases by a fixed percent each time period.
An example of compound decay is depreciation of a car over time.
The formula for compound decay is: A = P(1 - r/n)^(nt), where A represents the final amount, P is the principal amount, r is the annual decay rate (in decimal form), n is the number of times that the decay is compounded per unit t, and t is the time the object depreciates for.

Calculating Compound Growth and Decay

To calculate compound growth or decay, insert the given numbers into their correct places in the formula and solve for A.
This often involves the use of a calculator, so ensure you’re confident with using the power (^) function on your calculator.
Remember to convert any percentage increases or decreases into decimals before using them in the formula.

Understanding compound growth and decay is crucial for dealing with various real-world scenarios.
For example in finance, it helps in understanding how savings or loans grow over time. In science, it helps in understanding population growth or the decay of radioactive substances.
Also, in predicting future trends or outcomes, these mathematical models are essential.

Use a variety of exam-style questions and mathematical problems to practice and master these concepts.
Exam-style questions will help you familiarise with problem solving and how to apply these concepts in practical contexts.
Commit the formulas for compound growth and decay to memory. Regularly test yourself to ensure they’re ingrained.
In addition to practicing set problems, attempt further problems in other forms such as those found in word problems, various application scenarios and graphing problems.
Regular practice and revision are key to mastering compound growth and decay, and achieving your best possible results.