# Math 102/Chapter 6

### From charlesreid1

## Contents

- 1 Chapter 6: Exponential and Logarithmic Functions
- 1.1 Section 6.1: Composite Functions
- 1.2 Section 6.2: One to One Functions, Inverse Functions
- 1.3 Section 6.3: Exponential Functions
- 1.4 Section 6.4: Logarithmic Functions
- 1.5 Section 6.5: Properties of Logarithms
- 1.6 Section 6.6: Logarithmic and Exponential Equations
- 1.7 Section 6.7: Financial Models
- 1.8 Section 6.8: Growth Decay Models
- 1.9 Section 6.7: Building Exponential, Logarithmic, Logistic Models

- 2 Chapter 6 Objectives
- 3 Flags

# Chapter 6: Exponential and Logarithmic Functions

Chapter 6: Exponential/Log Functions

- Composition functions
- One to one functions and inverse functions
- Exponential functions
- Logarithmic functions
- Properties of logs
- Log and exponential equations
- Financial models
- Exponential growth and decay
- Logistic growth and decay
- Building log/exp models

## Section 6.1: Composite Functions

Definition of composite function

Evaluating composite function

Finding composite function and its domain

Finding domain of f o g

Finding composite function and its domain

Showing two composite functions are equal

Finding components of composite function

Finding components of composite function

## Section 6.2: One to One Functions, Inverse Functions

One to one function definition

Determining whether function is one-to-one

Horizontal line test

Using horizontal line test

Inverse function

Verifying inverse functions

Verifying inverse functions

Graphing inverse functions

How to find inverse function

Finding inverse function

Finding inverse of domain-restricted function

## Section 6.3: Exponential Functions

Using calculator to evaluate powers of 2

Intro to exponential growth

Identifying linear vs exponential functions

Graphing exponential function

Properties of exponential functions

Graphing an exponential function

Graphing exponential functions using transformations

Definition of the number e

Graphing exponential functions using transformations

Solving exponential equations

Solving exponential equations

Summary: Properties of the exponential function

## Section 6.4: Logarithmic Functions

Relating logs to exponents

Changing exponential equations to logarithmic equations

Changing log expr to exponential expr

Find exact value of log expr

Find domain of log function

Graph log function and its inverse

Graph a log function and its inverse

Solving log equations

Using logs to solve exponential equation

Summary: properties of the log function

## Section 6.5: Properties of Logarithms

Establishing properties of logarithms

Theorem: properties of logs

Using properties

Log of product equals sum of logs

Log of quotient equals diff of logs

Log of power equals product of power and log

Write log expr as sum of logs

Write log expr as diff of logs

Write log expr as sum and diff of logs

Write expr as single logarithm

Approximating a log with non-10 and non-e base

Using change of base formula

Summary: properties of logs

Logarithm history/invention

## Section 6.6: Logarithmic and Exponential Equations

Solving logarithmic equation

Solving logarithmic equation

Solving logarithmic equation

Solving exp equation

Solving exp equation

Solving exp equation quadratic in form

Solving eqn using graphing utility

## Section 6.7: Financial Models

Simple interest formula

Computing compound interest

Compound interest formula

Comparing investments using different compounding periods

Using continuous compounding

Rate of interest required to double investment

Time to double or triple investment

## Section 6.8: Growth Decay Models

Find equations of populations that obey law of uninhibited growth

Uninhibited growth of cells

Bacterial growth

Bacterial growth

Find equations of populations that obey law of decay

Estimating age of ancient tools

Using Newton's Law of cooling

Using logistic models

Logistic model definition

Properties of logistic model

Fruit fly population

Wood products

## Section 6.7: Building Exponential, Logarithmic, Logistic Models

Fitting an exponential function to data

Fitting a logarithmic function to data

Fitting logistic function to data

# Chapter 6 Objectives

Section 6.1:

- Form a composite function
- Form the domain of a composite function

Section 6.2:

- Determine whether a function is one-to-one
- Determine the inverse of a ffunction defined yb a map or a set of ordered pairs
- Obtain the graph of the inverse funciton from the graph of the funcitno
- Find the inverse of a funciton defined by an equation

Section 6.3

- Evaluate exponential functions
- Grha exp functions
- Define e

8 Solve exponential equations

Section 6.4

- Change exp statements to log statements and log statements to exp statements
- Evaluate log expressions
- Determine domain of log function
- Graph log functions
- Solve log equations

Section 6.5:

- Work with the properties of logs
- Write a log expression as a sum or difference of logs
- Write a log expression as a single log
- Evaluate logs whose base is neither 10 nor e

Section 6.6:

- Solve log equations
- Solve exponential equations
- Solve log and exponential equations using a graphing utility

Section 6.7:

- Determine the future value of a lump sum of money
- Calculate effective rates of return
- Determine the present value of a lump sum of money
- Determine the rate of interest or time required to double a lump sum of money

Section 6.8:

- Find equations of populations obeying law of uninhibited growth
- Find equations of populations obeying law of decay
- Use Newton's Law of Cooling
- Use logistic models

Section 6.9:

- Build exp model from data
- Build log model from data
- build logistic model from data

# Flags

Math 102 - College AlgebraChapter-by-chapter outline: Chapter 1: Equations and Inequalities Math 102/Chapter 1 Chapter 2: Graphs Math 102/Chapter 2 Chapter 3: Functions and their Graphs Math 102/Chapter 3 Chapter 4: Linear and Quadratic Functions Math 102/Chapter 4 Chapter 5: Polynomial and Rational Functions Math 102/Chapter 5 Chapter 6: Exponential/Log Functions Chapter 8: Systems of Equations and Inequalities Math 102/Chapter 8
Puzzles: Puzzles
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