Chapter 32.3
Continuous growth and decay
What You'll Learn
Apply the continuous compounding formula A = Pe^(rt) to solve growth and decay problems
Recognize when to use the constant e for continuously compounding interest calculations
Calculate final amounts using continuous growth with given principal, rate, and time
Determine decay rates using natural logarithms and half-life information
Solve exponential equations with e by applying natural log (ln) to both sides
What You'll Practice
1
Computing account balances with continuous compound interest over many years
2
Finding decay rates of radioactive substances given half-life
3
Using natural logarithms to solve for variables in exponents with base e
4
Interpreting continuous growth and decay in real-world contexts
Why This Matters
Continuous growth and decay models are essential for understanding real-world phenomena like compound interest, population growth, and radioactive decay. This formula appears throughout advanced math, physics, chemistry, and finance, making it crucial for STEM careers and higher-level coursework.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Skills
Exponential Growth
Exponential Decay
Continuous Compounding
Natural Logarithm
Half-Life
Euler's Number
Interest Rate Calculations
OH Curriculum Aligned
