Introduction to Exponential Functions and Logarithm Functions

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
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