- Subject:
- Mathematics
- Material Type:
- Module
- Provider:
- Ohio Open Ed Collaborative
- Tags:
- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Text/HTML
Chapter 6.1 - Exercises
Chapter 6.1 - Introduction to Exponential and Logarithmic Functions
Chapter 6.1 - Introduction to Exponential and Logarithmic Functions
Khan Academy - Exponential Functions
Khan Academy - Exponential Growth and Decay
Khan Academy - Graphing Exponential Functions
Khan Academy - Logarithmic Functions
Khan Academy - Rules of Exponents
Paul's Online Notes
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
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