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

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
• 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