Mastering Exponential and Logarithmic Functions

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!

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