Mathematics
July 22, 2026 · 10 min read
Exponential Functions: Modeling Growth and Decay
Evaluate and analyze exponential functions f(x) = a·b^x. Learn growth factors, asymptotes, and real-world applications.
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Exponential functions model quantities that grow or decay by a constant factor per unit change. The function f(x) = a·b^x is one of the most important in mathematics, appearing in finance, biology, physics, and engineering.
The Function
f(x) = a · b^x
Where a is the y-intercept and b is the growth/decay factor.
Key Properties
- Domain: all real numbers
- Range: (0, ∞) for a > 0
- Horizontal asymptote: y = 0
- Growth if b > 1, decay if 0 < b < 1
Applications
- Finance: Compound interest
- Biology: Population growth, bacterial reproduction
- Physics: Radioactive decay, cooling
- Epidemiology: Disease spread in early stages