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Teaching & Academics
Math
Mastering Exponential and Logarithmic Functions

Mastering Exponential and Logarithmic Functions

Loại khoá học: Teaching & Academics

Work with exponential and logarithmic functions like mathematicians do! Includes 130+ sample problems and solutions.

image
50.000 VND
70 VND
Đầy Đủ Bài Giảng
Học Online Tiện Lợi
Kích Hoạt Nhanh 2-5 Phút
Thanh toán tự động
Được phép tải xuống

Tổng quan

Nội dung khoá học

Đánh giá

Mô tả

Are you struggling with exponential or logarithmic equations in your mathematics or science class?  You've come to the right place!

This course will first help you to extend the basic principles of exponents to create functions modeling the real-world phenomena of growth and decay.  Not only will you use exponents to create these models, but after learning the principles of logarithms, you will be better prepared to solve advanced exponential equations using logarithms.  Additionally, you will use Euler's Number (the constant "e" which has a value of approximately 2.71828) and "natural" logarithms to work with and solve real-world problems involving continuous growth and decay.  With an understanding of the  principles of logarithms, you will be able to solve advanced exponential functions problems more efficiently and exactly than with other algebraic methods.  


Develop confidence with exponential functions, the basic concept of a logarithm and properties of logarithms, and how to apply both exponents and logarithmic principles to solve real-world problems.  This course builds on my previous course (Mastering Exponents, Exponential Expressions and Equations) and designed to supplement your existing and future mathematics and science classes.


General Topics Included in this course:


  • Review of principles of exponents

  • A review of function notation and meaning

  • Development of Exponential Function models of real-world phenomena

  • Using Euler's Number (e = 2.71828...) as a base in situations involving continuous growth or decay

  • Basics of Logarithms

  • Properties of Logarithms

  • Solving Logarithmic Equations

  • Solving Real-World Problems with Exponents and Logarithms


Exponents and Logarithms Are Powerful Mathematical Tools!

With an understanding of exponents, models can be established to determine how long it will take for a population to double, or how long it will take for a pie that has been taken out of the oven to cool to half of its temperature.   

If we know that an investment is earning 6% interest every year, we know that it will take 11.896 years to double in value.  We can also predict that if a forest is losing 5% of its trees each year due to a bark beetle infestation, and the process is continuous, it will only take about 13.86 years for the forest to reach its half-life, or the time at which half of its trees have been lost.

How  are such challenging problems solved?  Come and discover the principles that governing Exponential and Logarithmic Functions to solve these, and other real-world types of problems involving growth and decay.  As you master these useful tools, you will find greater success in your high school and college math and science courses. 


Content and Overview

All advanced Algebra-based mathematics courses and most science courses require a clear understanding of exponents and logarithms, so learning the fundamental principles of exponents and logarithms, and how they are related, opens up a new world of understanding for you and gives you a leg up in your studies.  This course was designed for high school and college level students who already understand the basic principles of exponents and can solve exponential functions by Algebraic processes.  However, these concepts are then expanded to include exponential functions, logarithms, logarithmic functions and how to use these principles to solve real-world problems involving growth and decay.  As you master these fundamental concepts, you will also form the basis for mastering other advanced mathematical topics such as logistic growth functions, Calculus and advanced polynomials.

In addition to topics listed previously, this course includes instruction on:


  • Requirements for exponential functions

  • "Parent" exponential growth and decay functions

  • Exponential and Logarithmic functions with negative exponents

  • Transformations of exponential functions

  • Domain and range of exponential and logarithmic functions

  • Growth and decay problems involving money

  • Graphing exponential and logarithmic equations

  • Use of a scientific and/or graphing calculator to solve problems (TI-84 modeled)

  • Half-lives (halving times) and doubling times

  • Asymptotes of exponential and logarithmic functions and their meanings

  • A development of Euler's Number and how Continuous Exponential Functions are developed from this quantity

  • The difference between continuous vs. periodic (non-continuous) growth and decay

  • Effective interest rates

  • How exponents and logarithms are inverse operations mathematically

  • The difference between natural (base "e") logarithms and common logarithms ("base 10")

  • Ph levels in Chemistry

  • Decibel Levels

  • Methods of solving exponential and logarithmic equations

  • Change of base

  • The Rule of 72's

  • Using exponents to guess a number between 1 and any power of 2 (a fun extension)

The course is designed with lessons, regular checks for understanding with solutions worked out in the videos.  In addition to myriad examples in the instruction, there are a total of 115 additional problems provided, 10 or more at the end of each section, by which to assess your understanding and progress.  Answers can be checked using the provided answer keys or you can follow along with me on video as I work out the solutions with you. 

I'm looking forward to working with you in this course!

Bạn sẽ học được gì

Understand the basics of logarithms and exponents

Create Scientific and Mathematical models involving exponents and logarithms

Solve simple and advanced Exponential Equations

Solve simple and advanced Logarithmic Equations

Use Exponents and Logarithms to solve real-world problems

130+ Provided problems and worked-out solutions

Yêu cầu

  • This class develops further the ideas found in my other course entitled Mastering Exponents, Exponential Expressions and Equations.
  • Familiarity with exponents, their properties and solving exponential equations.
  • Familiarity with graphing on the Cartesian Coordinate System
  • Solving basic algebraic equations
  • A document is provided (with solutions) for students to assess if they have the basic skills requirements

Nội dung khoá học

10 sections

Welcome to the Course!

2 lectures
Introduction
02:47
Assumed Skills Review for this Course
00:10

Exponential Functions

29 lectures
Section 2 Learning Goals
02:29
Review of Function Notation
02:31
Requirements of Exponential Functions
01:26
Link to Free Resource
00:19
Graphing the "Parent" Exponential Growth Function
10:35
Graphing the "Parent" Exponential Decay Function
05:01
Check for Understanding 1
05:33
Check for Understanding 2
01:21
Exponential Functions with Negative Exponents
09:35
Exponential Graph Transformations: Vertical Stretches
09:52
Exponential Graph Transformations: Horizontal Translations
07:43
Exponential Graph Transformations: Vertical Translations
06:18
Check for Understanding: Transformations
08:46
Horizontal Reflections Revisited
04:35
A Note on "Intermediate" or "Continuous" Values
03:01
Graphing Exponential Functions with Multiple Transformations part 1
08:49
Graphing Exponential Functions with Multiple Transformations Part 2
06:14
Domain and Range of Exponential Functions
08:17
Supplementary Resource: Using the TI-84 Graphing Calculator part 1
07:21
Supplementary Resource: Using the TI-84 Graphing Calculator part 2
08:46
Section 2 Practice Problems
00:12
Section 2 Problems #1 - 2 Worked Out
03:59
Section 2 Problems #3 - 5 Worked Out
06:45
Section 2 Problem #6 Worked Out
05:17
Section 2 Problems #7 - 8 Worked Out
03:06
Section 2 Problem #9 Worked Out
04:57
Section 2 Problems #10 - 11 Worked Out
07:48
Section 2 Problem #12 Worked Out
04:34
Congratulations on Completing Section 2!
00:10

Applications of Exponential Functions

29 lectures
Section 3 Learning Goals
02:00
Evaluating Exponential Expressions part 1
06:41
Evaluating Exponential Expressions part 2
05:12
Application: Interest
08:31
Application: Interest with Multiple Compounding Periods
10:04
Check for Understanding Part 1
06:40
Check for Understanding Part 2
01:59
Solving for Interest Rate
04:16
Solving for Time Periods
08:30
Exponential Decay Models part 1
05:19
Exponential Decay Models part 2
03:15
Finding Initial Amount, Decay Rate and Time Periods part 1
05:07
Finding Initial Amount, Decay Rate and Time Periods part 2
07:45
Check for Understanding Part 1
06:44
Check for Understanding Part 2
05:18
Graphing Exponential Functions part 1
01:13
Graphing Exponential Functions part 2
12:06
Graphing Exponential Functions part 3
04:51
Solving Exponential Functions by Graphing
10:09
Section 3 Practice Problems
00:12
Section Problems #1 - 5 Worked Out
06:39
Section Problem #6 Worked Out
07:01
Section Problem #7 Worked Out
04:22
Section Problem #8 Worked Out
06:02
Section Problem #9 Worked Out
07:38
Section Problem #10 Worked Out
07:21
Section Problem #11 Worked Out
06:10
Section Problem #12 Worked Out
05:33
Congratulations on Completing Section 3!
00:11

Finding Exponential Models

21 lectures
Section 4 Learning Goals
01:41
Review: Finding Initial Value
03:49
Finding Growth or Decay Rate and Initial Amount part 1
07:25
Finding Growth or Decay Rate and Initial Amount part 2
03:40
Check for Understanding
04:06
Finding Equation with an Asymptote (Not Equal to Zero)
06:59
Check for Understanding
04:08
Doubling Times part 1
05:42
Doubling Times part 2
05:27
Half-Lives (Halving Times) part 1
03:09
Half-Lives (Halving Times) part 2
04:52
A Reminder about Domain and Range
04:13
Domain and Range from Context
07:10
Section 4 Practice Problems
00:12
Section 4 Problems #1 - 2 Worked Out
03:50
Section 4 Problem #3 Worked Out
07:27
Section 4 Problems #4 - 5 Worked Out
05:50
Section 4 Problems #6 - 8 Worked Out
11:29
Section 4 Problems #9 - 12 Worked Out
07:17
Section 4 Problems #13 - 18 Worked Out
05:32
Congratulations on Completion Section 4!
00:10

The Natural Base "e" (Euler's Number)

24 lectures
Section 5 Learning Goals
02:49
The Natural Base: Euler's Number (e)
04:53
Continuous Exponential Models
08:33
Derivation of Continuous Models (Optional)
09:08
Continuous vs. Non-Continuous Models part 1
02:50
Continuous vs. Non-Continuous Models part 2
13:53
Check for Understanding
10:20
Rules of Exponents and the Natural Base part 1
09:03
Rules of Exponents and the Natural Base part 2
05:59
Finding Models with the Natural Base e
04:11
Check for Understanding part 1
03:52
Check for Understanding part 2
03:07
Effective Interest Rate part 1
05:18
Effective Interest Rate part 2
05:17
Section 5 Practice Problems
00:12
Section 5 Problems #1 - 2 Worked Out
08:09
Section 5 Problem #3 Worked Out
06:37
Section 5 Problem #4 Worked Out
05:56
Section 5 Problem #5 Worked Out
04:19
Section 5 Problem #6 Worked Out
04:00
Section 5 Problem #7 Worked Out
04:29
Section 5 Problem #8 Worked Out
04:19
Section 5 Problems #9 - 10 Worked Out
07:09
Congratulations on Completion Section 5!
00:10

Logarithm Basics

23 lectures
Section 6 Learning Goals
01:45
Representing Logarithms
03:19
Check for Understanding
01:56
Exponential and Logarithmic Forms
03:32
Natural and Common Logarithms
03:42
Using a Calculator to Evaluate Logarithms
04:04
Application: Ph Levels
09:05
Check for Understanding
08:19
How Exponential and Logarithmic Functions are Inverses of One Another part 1
04:15
How Exponential and Logarithmic Functions are Inverses of One Another part 2
07:03
Graphing Logarithmic Functions
08:14
Check for Understanding
04:13
Alternate Way to Find Points when Graphing Logarithmic Functions
02:32
Section 6 Practice Problems
00:12
Section 6 Problems #1 - 4 Worked Out
03:34
Section 6 Problems #5 - 6 Worked Out
03:13
Section 6 Problems #7 - 8 Worked Out
05:23
Section 6 Problems #9 - 10 Worked Out
02:26
Section 6 Problems #11 - 12 Worked Out
05:20
Section 6 Problem #13 Worked Out
03:02
Section 6 Problems #14 Worked Out
03:23
Section 6 Problems #15 - 17 Worked Out
09:33
Congratulations on Completion Section 6!
00:18

Properties of Logarithms

29 lectures
Section 7 Learning Goals
01:28
Equal Bases and Antilogs Cancel One Another part 1
04:27
Equal Bases and Antilogs Cancel One Another part 2
05:20
Changing the Base
08:41
Overview of Power, Product and Quotient Rules
04:11
Product Rule Examples
03:00
Power Rule Examples
02:15
Quotient Rule Examples
03:11
Check for Understanding
02:16
Expanding Logarithmic Expressions part 1
06:19
Expanding Logarithmic Expressions part 2
07:04
Condensing Logarithmic Expressions
08:19
Check for Understanding part 1
03:21
Check for Understanding part 2
09:58
Application: Decibel Levels
05:24
Check for Understanding part 1
05:58
Check for Understanding part 2
07:18
Use Given Information and Properties to Evaluate Expressions part 1
09:37
Use Given Information and Properties to Evaluate Expressions part 2
05:10
Section 7 Practice Problems
00:12
Section 7 Problems #1 - 2 Worked Out
03:50
Section 7 Problems #3 - 4 Worked Out
06:59
Section 7 Problem #5 Worked Out
08:40
Section 7 Problem #6 Worked Out
07:53
Section 7 Problems #7 - 8 Worked Out
08:49
Section 7 Problem #9 Worked Out
06:41
Section 7 Problems #10 - 11 Worked Out
05:59
Section 7 Problem #12 Worked Out
05:03
Congratulations on Completing Section 7!
00:11

Solving Logarithmic Equations

32 lectures
Section 8 Learning Goals
01:33
Solving Logarithmic Equations by Switching to Exponential Form
07:18
Solving Logarithms with the Same Base part 1
10:34
Check for Understanding
05:22
Solving Using Change of Base
04:31
Solving Equations Written in Exponential Form
02:13
Solving More Complex Equations Written in Exponential Form
06:07
Check for Understanding
05:41
Solving Equations by Taking the Logarithm of Both Sides
06:21
Solving More Complex Equations by Taking the Logarithm of Both Sides
15:02
Check for Understanding
09:29
Using Properties of Logarithms to Solve Equations part 1
10:20
Using Properties of Logarithms to Solve Equations part 2
09:50
Challenge/Extension: Quadratic Logarithm Problems
07:43
Check for Understanding
04:34
Application: Decibels Revisited
05:18
Check for Understanding
05:40
Section 8 Practice Problems
00:12
Section 8 Problem #1 Worked
03:38
Section 8 Problem #2 Worked
02:55
Section 8 Problem #3 Worked
02:40
Section 8 Problem #4 Worked
06:10
Section 8 Problem #5 Worked
04:40
Section 8 Problem #6 Worked
07:08
Section 8 Problem #6b Worked
05:40
Section 8 Problem #7 Worked
06:10
Section 8 Problem #8 Worked
04:56
Section 8 Problem #9 Worked
01:37
Section 8 Problem #10 Worked
02:25
Section 8 Problems #11 - 12 Worked
03:56
Section 8 Problems #13 - 14 Worked
03:25
Congratulations on Completion Section 8!
00:11

Solving Real-World Problems with Logarithms

50 lectures
Section 9 Learning Goals
01:55
An Analogy: Krunch and the Stone Giant
02:23
Basic Exponential Growth and Decay Formulas
06:26
Ways to Solve the "Krunch" Problem
07:19
Graphing Parent Decay Functions
05:01
Krunch Shrinks Down - Solving for Time
09:21
Check for Understanding
08:35
Application: Money-Related Problems
06:19
Application: Money-Related Problems Using Other Models
03:15
Using Formulas to Solve Money-Related Equations
05:44
Money Problems: How Long Will It Take?
09:21
Check for Understanding
10:13
Application: Scientific Growth
07:37
Application: Scientific Decay
04:12
Additional Examples to Consider
07:45
Check for Understanding
09:12
Finding an Exponential Growth Model from 2 Data Points
09:27
Finding a Continuous Growth Model from 2 Data Points
09:09
Check for Understanding part 1
07:00
Check for Understanding part 2
05:54
Decay Models with a Known Half-Life
08:20
Finding Doubling Times in Growth Models
04:46
Check for Understanding part 1
04:21
Check for Understanding part 2
05:24
Application: The Rule of 72s
02:05
More on the Rule of 72s
01:42
Application: Guessing a Number
04:31
Example of Guessing a Number
04:24
Check for Understanding
06:44
Guessing a Number: A Word on Technique
02:11
Section 9 Practice Problems
00:12
Section 9 Problems #1 - 2 Worked Out
05:53
Section 9 Problem #3 Worked Out
03:08
Section 9 Problem #4 Worked Out
04:14
Section 9 Problem #5 Worked Out
07:25
Section 9 Problem #6 Worked Out
04:47
Section 9 Problem #7 Worked Out
02:21
Section 9 Problem #8 Worked Out
07:49
Section 9 Problem #9 Worked Out
04:20
Section 9 Problem #10 Worked Out
06:35
Section 9 Problem #11 Worked Out
05:01
Section 9 Problem #12 Worked Out
07:36
Section 9 Problem #13 Worked Out
07:01
Section 9 Problem #14 Worked Out
05:29
Section 9 Problem #15 Worked Out
09:29
Section 9 Problem #15 Extension Worked Out
02:36
Section 9 Problems #16 - 18 Worked Out
04:16
Section 9 Problem #19 Worked Out
07:20
Section 9 Problem #20 Worked Out
08:52
Congratulations on Completing Section 9!
00:11

Congratulations on Completing Mastering Exponential and Logarithmic Equations!

1 lectures
Congratulations from your instructor!
01:13

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