Exponential Functions
Exponential and logarithm functions are the basis for the study of growth and decay phenomena such as
- Growth or decay of investment, Compound Interest
- Growth or decay of a population
- Radioactive decay
- Etc.
Both functions are one-to-one and are inverses of each other. First we study exponential functions.
Review: Laws of Exponents, domain and range of one-to-one functions and their inverses
Learning Objectives:
- Study and understand the basic exponential function \(f(x) = b^x, b > 0, b \neq 1\)
- Domain, Range, Intercepts, Asymptote and Graph
- Apply transformations to study general exponential functions \(f(x) = a \cdot b^{mx + c} + d\)
- Domain, Range, Intercepts, Asymptote and Graph
- Study and understand the natural exponential function \(f(x) = e^x\)
- Solve applications using exponential functions