24.02.2022, 10:41
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Mastering Exponential and Logarithmic Functions
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 9.98 GB | Duration: 21h 19m
Work with exponential and logarithmic functions like mathematicians do! Includes 130+ sample problems and solutions.
What you'll learn
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
Requirements
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
Description
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!
Who this course is for
High school or college students needing help understanding Exponents, Exponential Functions, Logarithms and Logarithmic Functions.
Anyone needing to apply principles of Exponents and Logarithms to model and solve typical and advanced real-world problems.
Homepage
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