Grade 12 · Mathematics
Exponential functions
Why it matters
Growth and decay.
Advanced20m readingPrerequisite: None
What is an exponential function?
Short answer
An exponential function has the form y = a·bˣ, where the variable is in the exponent and the base b is a positive constant. When b > 1 the function models growth; when 0 < b < 1 it models decay. Exponential functions change by a constant factor over equal intervals, which is why they describe population growth, compound interest, and radioactive decay.
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Frequently asked questions
- What is the difference between exponential growth and decay?
- Growth occurs when the base is greater than 1; decay occurs when the base is between 0 and 1.
- How is an exponential function different from a power function?
- In an exponential function the variable is the exponent (bˣ); in a power function the variable is the base (xⁿ).