Overview
This lecture explains how to use the rule of 70 to calculate the doubling time of a population or investment based on its growth rate, with step-by-step example problems.
The Rule of 70
- The rule of 70 estimates the doubling time for a quantity growing at a constant percentage rate.
- To calculate doubling time, divide 70 by the annual percentage growth rate.
Example Problems
- For a 10% growth rate: 70 ÷ 10 = 7 years to double.
- For a 2% growth rate: 70 ÷ 2 = 35 years to double.
- If a population doubles every 5 years, set up the equation: 70 ÷ P = 5.
- Solve for P: 5P = 70 → P = 14%, so the growth rate is 14%.
Application Problem: Rabbits Example
- Given a 4% annual population growth rate, doubling time is 70 ÷ 4 = 17.5 years.
- The closest answer is 17 years.
Key Terms & Definitions
- Rule of 70 — A formula to estimate doubling time: 70 ÷ percentage growth rate.
- Doubling time — The period required for a quantity growing exponentially to double in size.
- Growth rate — The percent increase per time period, usually per year.
Action Items / Next Steps
- Practice using the rule of 70 with different growth rates and doubling times.
- Review related textbook sections on exponential growth and the rule of 70.