Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Mathematics, Tmm0022
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Text/HTML

Introduction to Exponential Functions and Logarithm Functions

Section 1: 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

Section 2: Introduction to Logarithmic Functions

A Logarithmic function with base b, where b > 0 and b is not equal to 1, is the inverse of the corresponding exponential function. These functions are useful in the study of computer algorithms and natural growth/decay phenomena of living beings, among other applications.

Learning Objectives:

  • Study and understand the basic logarithmic function \(f(x) = b^x\)
    • Domain, Range, Intercepts, Asymptote and Graph
  • Study and understand the basic logarithmic function \(a \cdot b^{mx + b} + d\) where \(b > 0, b\neq 1\)
    • Domain, Range, Intercepts, Asymptote and Graph
  • Learn and apply basic properties of logarithms
  •  \(b^a = c\) if and only if \(log_b(c) =a\)
  • \(log_{b} b^x = x\) for all x and \(b^{log_{b} x} = x \) for x > 0