# 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