Exponential Growth and Decay
Exponential growth and decay occur when a quantity changes by a constant percentage each period. Population growth, radioactive decay, and compound interest are all exponential processes.
What You Need to Know
Key Concept Diagram
Exponential growth: A = A0 x r^n, where r > 1
Exponential decay: A = A0 x r^n, where 0 < r < 1
The growth/decay factor r = 1 + (percentage/100) for growth, or 1 - (percentage/100) for decay
Exponential growth starts slowly then accelerates rapidly
Key Vocabulary
Exponential growth
Growth where the rate of increase is proportional to the current value
Decay factor
The multiplier (less than 1) applied each period in exponential decay
Growth factor
The multiplier (greater than 1) applied each period in exponential growth
Initial value
The starting value A0 before any growth or decay occurs
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A population of 500 bacteria doubles every hour. How many will there be after 4 hours?
Question 2
A car worth $20,000 depreciates by 15% per year. What is its value after 2 years?
Question 3
Which describes exponential growth correctly?
Key Concepts Summary
- ●Exponential growth: A = A0 x r^n, where r > 1
- ●Exponential decay: A = A0 x r^n, where 0 < r < 1
- ●The growth/decay factor r = 1 + (percentage/100) for growth, or 1 - (percentage/100) for decay
- ●Exponential growth starts slowly then accelerates rapidly