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Exponential Growth and Decay by a Factor
See how the growth or decay factor in an exponential function tells you whether a quantity is increasing or shrinking, and by how much each step.
What You'll Learn
Exponential growth and decay both follow the formula y = a(b)^x, where a is the starting value and b is the growth or decay factor
A growth factor is greater than 1 and makes the quantity increase every step
A decay factor is between 0 and 1 and makes the quantity decrease every step
The factor b is multiplied repeatedly, which is what makes the change accelerate instead of staying constant
Word problems usually give you the starting amount, the factor (or a way to find it), and a time variable x
What You'll Practice
1
Building exponential growth models from word problems about populations
2
Converting weeks to years and other time unit conversions
3
Calculating future values using exponential equations with fractional exponents
4
Rounding decimal answers to whole numbers for discrete quantities
Why This Matters
Understanding growth and decay factors is essential for modeling real-world situations like population growth, compound interest, radioactive decay, and medication dosage. This exponential thinking appears throughout advanced math, science, finance, and helps you make informed decisions about investments and loans.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Exponential Growth
Growth Factor
Exponential Models
Unit Conversion
Exponents
Word Problems
Population Modeling
ON Curriculum Aligned