# College Algebra with Current Interesting Applications and Facts

**Author(s):**
Gisela
Acosta
,
Margie
Karwowski

**Edition:
**
1

**Copyright:
**
2012

**Pages:
**
666

**Edition:
**
2

**Copyright:
**
2021

**Edition:
**
2

**Copyright:
**
2021

**Pages:
**
666

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* College Algebra with Current Interesting Applications and Facts* provides students the opportunity to experience real-life settings and work on activities that model real-world situations, while capturing the student’s interest. This text contains application problems which are based on current everyday life settings and topics interesting to college-age students, including Facebook, smartphones, online games, digital world, and origin of text messaging, to name a few. The real-world data contains the corresponding sources, along with an interesting fact about the topic, which allows students to feel they have learned something outside of math as well.

* College Algebra with Current Interesting Applications and Facts* helps students to solidify reasoning and problem-solving skills, while demonstrating how college algebra can model real-world scenarios. The textbook encompasses multiple approaches to problem solving including verbal, numerical, symbolic, and graphical approaches.

The NEW second edition of ** College Algebra with Current Interesting Applications and Facts** by Gisela Acosta and Margie Karwowski:

- Integrates a “Getting Started” section at the beginning of each chapter to help students review concepts and techniques.
- Provides “in-class practice” problems that can be used for class discussion, review of topics, discovery of concepts, and homework practice.
- Contains numerous exercises and applications, as well as a chapter review in each section.
- Includes Caution notes identifying where “friendly errors” tend to occur and how to avoid them.
- Offers access to online homework that corresponds with problems and material from the text.

**Chapter 1 Linear Functions and Mathematical Modeling **

1.0 Getting Started

Graphing Calculator Basics ◾ Basic Graphing Calculator Functions (Models TI-84, TI-84 Plus) ◾ Graphing Lines with the Graphing Calculator ◾ Basic Viewing Windows Under the Zoom Key ◾ Creating a Table of Values with the Grapher ◾ Interval Notation

1.1 Linear Equations and Intercepts

x-and y-Intercepts of a Line ◾ Standard Form of a Line ◾ Graphing Lines Using Intercepts

1.2 Slope of a Line, Vertical Intercept, and Rate of Change

Slope of a Line ◾ Slope and the Graph of a Line ◾ The Slope- Intercept Form of a Line ◾ Slope as Rate of Change

1.3 Functions: Definition, Notation, and Evaluation

Verbal Description ◾ Numeric Description ◾ Symbolic Description ◾ Graphical Description ◾ Domain and Range of a Function ◾ Restricting Domains in Terms of Context ◾ Function Notation ◾ Evaluating a Function

1.4 Interpreting and Evaluating Functions Using Graphs

Identifying Domain and Range from a Graph ◾ Vertical Line Test ◾ Increasing, Decreasing, and Constant Functions

1.5 Linear Functions: Equations and Graphs

Finding the Equation of a Linear Function ◾ Point-Slope Form of a Line ◾ Equations of Horizontal and Vertical Lines ◾ Parallel and Perpendicular Lines

1.6 Lines of Best Fit

Scatterplots ◾ Lines of Best Fit and Modeling ◾ Finding Linear Regression Models with the Graphing Calculator

Chapter 1 Summary

Chapter 1 Review

**Chapter 2 Linear Systems in Two Variables and Inequalities with Applications **

2.0 Getting Started

Solving Linear Equations by Graphing ◾ Solving Linear Equations by the Tabular Method (Numerical Solutions) ◾ Properties of Linear Inequalities in One Variable

2.1 Graphical and Numerical Solutions

Solving a Linear System in Two Variables by Graphing ◾ Classification of Linear Systems ◾ Three Case Scenarios for Linear Systems ◾ Numerical Solutions of Linear Systems in Two Variables

2.2 Substitution and Elimination

Solving a Linear System in Two Variables by Substitution ◾ Solving a Linear System in Two Variables by Elimination ◾ Identifying Inconsistent and Dependent Systems Algebraically

2.3 Linear Inequalities in Two Variables

Graphical Solutions and Applications ◾ Using the Graphing Calculator to Graph Linear Inequalities in Two Variables

2.4 Systems of Linear Inequalities

Solving a System of Linear Inequalities in Two Variables

Chapter 2 Summary

Chapter 2 Review

**Chapter 3 Non-Linear Functions and Applications**

3.0 Getting Started 192

Simplifying Expressions with Absolute Value ◾ Basic Operations with Polynomials ◾ Addition and Subtraction ◾ Multiplication ◾ Graphical Solutions of Inequalities

3.1 Basic Functions and Their Graphs

Graphing Basic Functions with the Graphing Calculator ◾ Function Symmetry: Even and Odd Functions ◾ Finding Relative Maximum and Relative Minimum Values ◾ Finding Relative Minima and Maxima with the Graphing Calculator ◾ Finding Zeros of a Function Graphically ◾ Finding Zeros of a Function with the Graphing Calculator

3.2 Transformations

Vertical Shifts ◾ Horizontal Shifts ◾ Reflections ◾ Stretching and Compressing Graphs of Functions ◾ Combining Multiple Transformations to Sketch a Graph ◾ Average Rate of Change ◾ The Difference Quotient

3.3 Piecewise-Defined Functions

Graphing Piecewise-Defined Functions ◾ Using the Graphing Calculator

3.4 Absolute Value Equations and Inequalities

Solving Absolute Value Equations ◾ Solving Absolute Value Inequalities

Chapter 3 Summary

Chapter 3 Review

**Chapter 4 Quadratic Functions and Various Nonlinear Topics**

4.0 Getting Started

Factoring ◾ Greatest Common Factor ◾ Factoring by Grouping ◾ Factoring Trinomials with a Leading Coefficient of 1 ◾ Factoring Trinomials Whose Leading Coefficient Is not 1 ◾ Factoring by Recognizing Patterns ◾ Radicals and Rational Exponents ◾ Operations with Radicals ◾ Rationalizing the Denominator ◾ Complex Numbers ◾ Operations with Complex Numbers ◾ Power of i ◾ Graphing Calculator and Complex Numbers

4.1 Solving Quadratic Equations

Solving Quadratic Equations by Factoring ◾ Projectiles and Gravity Models ◾ Solving Quadratic Equations by the Square Root Method ◾ Solving Quadratic Equations by Completing the Square ◾ Solving Quadratic Equations by the Quadratic Formula ◾ Quadratic Equations with Complex Solutions ◾ Nature of the Solutions of Quadratic Equations ◾ Quadratic Equations: Graphical and Numerical Solutions ◾ Summary of Solving Methods

4.2 Parabolas and Their Applications

The Vertex and Axis of Symmetry ◾ Intercepts of a Quadratic Function ◾ Sketching the Graph of a Quadratic Function ◾ The Vertex Form of a Quadratic Function ◾ Finding the Equation of a Quadratic Function ◾ Average Rate of Change

4.3 Quadratic Inequalities

Solving a Quadratic Inequality by Graphing ◾ Solving a Quadratic Inequality Algebraically ◾ Summary of Solving Methods

4.4 Other Types of Equations

Radical Equations ◾ Solving Radical Equations Algebraically ◾ Solving Radical Equations Graphically ◾ Solving Radical Equations Numerically ◾ Equations Reducible to Quadratic Form ◾ Rational Equations

4.5 Distance Formula, Midpoint Formula, and Circles

Distance Formula ◾ Midpoint Formula ◾ Circles ◾ Standard Form of the Equation of a Circle ◾ Graphing Circles ◾ General Form of the Equation of a Circle ◾ Graphing Calculator and Circles

4.6 Nonlinear Systems of Equations

Solving by Graphing ◾ Solving by Substitution ◾ Solving by Elimination ◾ Nonlinear Systems with Complex Solutions

4.7 Graphing Nonlinear Inequalities in Two Variables

Nonlinear Inequalities ◾ Graphing

Chapter 4 Summary

Chapter 4 Review

**Chapter 5 Inverse Functions and Applications**

5.0 Getting Started

Literal Equations ◾ Evaluating Functions

5.1 Finding the Inverse: Numerical, Graphical, and Symbolic Approaches

One-to-One Functions ◾ Inverse Functions ◾ Graphs of Inverse Functions ◾ Inverse Functions with Restricted Domains

5.2 Composition of Functions

Algebra of Functions ◾ Composition of Functions ◾ Composite Functions with the Graphing Calculator ◾ Decomposing Functions

5.3 Determining the Inverse Using Composition of Functions

Functions that Are Inverses of Each Other

Chapter 5 Summary

Chapter 5 Review

**Chapter 6 Exponential and Logarithmic Functions and Applications **

6.0 Getting Started

Laws of Exponents ◾ Scientific Notation

6.1 Exponential Functions and Their Graphs

Graphing Exponential Functions ◾ Transformations of Graphs of Exponential Functions ◾ Introduction to Exponential Growth and Decay ◾ Increasing or Decreasing by a Constant Percent ◾ Average Rate of Change ◾ Different Time Periods ◾ Comparing Linear and Exponential Growth

6.2 Logarithmic Functions and Their Graphs

Definition of Logarithm ◾ Evaluating Logarithms ◾ Common Logarithms ◾ Logarithmic Functions ◾ Graphing Logarithmic Functions ◾ Transformations of Graphs of Logarithmic Functions ◾ Some Applications of Logarithmic Functions

6.3 The Natural Exponential and Logarithmic Functions

The Natural Exponential Function ◾ The Natural Logarithmic Function ◾ Basic Properties of Natural Logarithms ◾ Graphs of Natural Logarithmic Functions

6.4 Exponential and Logarithmic Equations

Solving Exponential Equations with the Exponential Equality Property ◾ Solving Exponential Equations with Base 10 or Base e ◾ Solving Exponential Equations Graphically and Numerically ◾ Fundamental Properties of Logarithms ◾ Solving Exponential Equations Using Properties of Logarithms ◾ Solving Logarithmic Equations ◾ Solving Literal Equations Involving Exponential and Logarithmic Equations ◾ Change of Base Formula

6.5 Additional Exponential and Logarithmic Models

Compound Interest and Present Value ◾ Continuous Compounding and Present Value ◾ Doubling Time ◾ Annuities ◾ Amortization ◾ Logistic Function ◾ Carbon-14 Dating

Chapter 6 Summary

Chapter 6 Review

**Chapter 7 Polynomial and Rational Functions with Applications**

7.0 Getting Started

Factoring the Sum or Difference of Two Cubes ◾ Simplifying Rational Expressions

7.1 Polynomial Functions and Their Graphs

Graphs of Polynomial Functions ◾ Zeros (x-intercepts) of Polynomial Functions ◾ Properties of Polynomial Graphs ◾ Finding a Polynomial Function Given Its Graph ◾ Division of Polynomials ◾ Synthetic Division ◾ The Remainder Theorem

7.2 Rational Functions and Their Graphs

Graphs of Rational Functions and Asymptotes ◾ Using Transformations to Sketch the Graph of a Rational Function ◾ Sketching the Graph of a Rational Function ◾ Holes in Graphs of Rational Functions ◾ Finding a Rational Function Given Its Graph

7.3 Solving Polynomial and Rational Inequalities

Polynomial Inequalities ◾ Solving by Graphing ◾ Solving Algebraically ◾ Rational Inequalities ◾ Solving Rational Inequalities by Graphing ◾ Solving Rational Inequalities Algebraically

7.4 Variation

Direct Variation ◾ Inverse Variation ◾ Joint Variation ◾ Combined Variation

Chapter 7 Summary

Chapter 7 Review

**Index**

**Gisela Acosta**

Gisela Acosta holds a Bachelor of Arts, Master of Arts, and Ed.D. with majors in Curriculum, Music, and Mathematics from the University of Puerto Rico. Her doctorate degree dissertation in Mathematics Curriculum and perfect GPA earned her the UPR President’s Award for Academic Excellence. Dr. Acosta has received numerous awards for Excellency as a Mathematics Professor, and as Chair of the Department of Mathematics and Natural Sciences at the Inter American University of PR. Other awards include the NISOD Excellence in Learning Leadership Award, Distinguished Educator by the Phi Delta Kappa Honorary Society of Education, Excellency as Project Director for Title II and Title III Grants, Department of Education Special award for outstanding leadership as Consultant for the Development and Implementation of “Centers for Research in Mathematics Education,” and many other recognitions.

Dr. Acosta’s career as a Math Professor includes 21 years at the Inter American University of PR, and Valencia College, in Orlando, FL, where she has been a math professor since 1996. She has taught a wide variety of mathematics courses, from the developmental levels to advanced calculus and other advanced math courses. She has presented numerous workshops and conferences on mathematics and authored and co-authored other math publications. Dr. Acosta dedicates this second edition to Luis, her loving husband in Heaven (1944-2020).

**Margie Karwowski**

Margie Fernandez-Karwowski earned a Bachelor of Science and Master of Science in Applied Mathematics from the University of Akron and University of Central Florida, respectively. Her career in the teaching profession encompasses 20 years as a tutor, teacher, and professor at the high school, college, and university levels. Professor Karwowski’s career began at the Pre-Algebra level when she fi rst entered college. With hard work, effort, devotion, and motivated by challenge, she set her mind to pursue a career in the field of mathematics.

In 1983, fresh out of high school, Professor Karwowski backpacked throughout Western and Eastern Europe, experiencing other cultures for one month. From 1996 through 1999 she lived in Warsaw, Wiesbaden, and Budapest with her 2 children, which provided her a better appreciation of history and the world around her. These experiences helped the authors realize the need to incorporate a wide variety of subjects and topics into the mathematics classroom, which serves such a diverse student population. While living in Europe, Professor Karwowski participated in fundraisers for local orphanages which included writing a cookbook that featured international cuisine, with funds going to a home for children with AIDS. Professor Karwowski and her husband stay busy with their 5 kids and 2 grandchildren, and continue to volunteer helping the homeless and the elderly.

* College Algebra with Current Interesting Applications and Facts* provides students the opportunity to experience real-life settings and work on activities that model real-world situations, while capturing the student’s interest. This text contains application problems which are based on current everyday life settings and topics interesting to college-age students, including Facebook, smartphones, online games, digital world, and origin of text messaging, to name a few. The real-world data contains the corresponding sources, along with an interesting fact about the topic, which allows students to feel they have learned something outside of math as well.

* College Algebra with Current Interesting Applications and Facts* helps students to solidify reasoning and problem-solving skills, while demonstrating how college algebra can model real-world scenarios. The textbook encompasses multiple approaches to problem solving including verbal, numerical, symbolic, and graphical approaches.

The NEW second edition of ** College Algebra with Current Interesting Applications and Facts** by Gisela Acosta and Margie Karwowski:

- Integrates a “Getting Started” section at the beginning of each chapter to help students review concepts and techniques.
- Provides “in-class practice” problems that can be used for class discussion, review of topics, discovery of concepts, and homework practice.
- Contains numerous exercises and applications, as well as a chapter review in each section.
- Includes Caution notes identifying where “friendly errors” tend to occur and how to avoid them.
- Offers access to online homework that corresponds with problems and material from the text.

**Chapter 1 Linear Functions and Mathematical Modeling **

1.0 Getting Started

Graphing Calculator Basics ◾ Basic Graphing Calculator Functions (Models TI-84, TI-84 Plus) ◾ Graphing Lines with the Graphing Calculator ◾ Basic Viewing Windows Under the Zoom Key ◾ Creating a Table of Values with the Grapher ◾ Interval Notation

1.1 Linear Equations and Intercepts

x-and y-Intercepts of a Line ◾ Standard Form of a Line ◾ Graphing Lines Using Intercepts

1.2 Slope of a Line, Vertical Intercept, and Rate of Change

Slope of a Line ◾ Slope and the Graph of a Line ◾ The Slope- Intercept Form of a Line ◾ Slope as Rate of Change

1.3 Functions: Definition, Notation, and Evaluation

Verbal Description ◾ Numeric Description ◾ Symbolic Description ◾ Graphical Description ◾ Domain and Range of a Function ◾ Restricting Domains in Terms of Context ◾ Function Notation ◾ Evaluating a Function

1.4 Interpreting and Evaluating Functions Using Graphs

Identifying Domain and Range from a Graph ◾ Vertical Line Test ◾ Increasing, Decreasing, and Constant Functions

1.5 Linear Functions: Equations and Graphs

Finding the Equation of a Linear Function ◾ Point-Slope Form of a Line ◾ Equations of Horizontal and Vertical Lines ◾ Parallel and Perpendicular Lines

1.6 Lines of Best Fit

Scatterplots ◾ Lines of Best Fit and Modeling ◾ Finding Linear Regression Models with the Graphing Calculator

Chapter 1 Summary

Chapter 1 Review

**Chapter 2 Linear Systems in Two Variables and Inequalities with Applications **

2.0 Getting Started

Solving Linear Equations by Graphing ◾ Solving Linear Equations by the Tabular Method (Numerical Solutions) ◾ Properties of Linear Inequalities in One Variable

2.1 Graphical and Numerical Solutions

Solving a Linear System in Two Variables by Graphing ◾ Classification of Linear Systems ◾ Three Case Scenarios for Linear Systems ◾ Numerical Solutions of Linear Systems in Two Variables

2.2 Substitution and Elimination

Solving a Linear System in Two Variables by Substitution ◾ Solving a Linear System in Two Variables by Elimination ◾ Identifying Inconsistent and Dependent Systems Algebraically

2.3 Linear Inequalities in Two Variables

Graphical Solutions and Applications ◾ Using the Graphing Calculator to Graph Linear Inequalities in Two Variables

2.4 Systems of Linear Inequalities

Solving a System of Linear Inequalities in Two Variables

Chapter 2 Summary

Chapter 2 Review

**Chapter 3 Non-Linear Functions and Applications**

3.0 Getting Started 192

Simplifying Expressions with Absolute Value ◾ Basic Operations with Polynomials ◾ Addition and Subtraction ◾ Multiplication ◾ Graphical Solutions of Inequalities

3.1 Basic Functions and Their Graphs

Graphing Basic Functions with the Graphing Calculator ◾ Function Symmetry: Even and Odd Functions ◾ Finding Relative Maximum and Relative Minimum Values ◾ Finding Relative Minima and Maxima with the Graphing Calculator ◾ Finding Zeros of a Function Graphically ◾ Finding Zeros of a Function with the Graphing Calculator

3.2 Transformations

Vertical Shifts ◾ Horizontal Shifts ◾ Reflections ◾ Stretching and Compressing Graphs of Functions ◾ Combining Multiple Transformations to Sketch a Graph ◾ Average Rate of Change ◾ The Difference Quotient

3.3 Piecewise-Defined Functions

Graphing Piecewise-Defined Functions ◾ Using the Graphing Calculator

3.4 Absolute Value Equations and Inequalities

Solving Absolute Value Equations ◾ Solving Absolute Value Inequalities

Chapter 3 Summary

Chapter 3 Review

**Chapter 4 Quadratic Functions and Various Nonlinear Topics**

4.0 Getting Started

Factoring ◾ Greatest Common Factor ◾ Factoring by Grouping ◾ Factoring Trinomials with a Leading Coefficient of 1 ◾ Factoring Trinomials Whose Leading Coefficient Is not 1 ◾ Factoring by Recognizing Patterns ◾ Radicals and Rational Exponents ◾ Operations with Radicals ◾ Rationalizing the Denominator ◾ Complex Numbers ◾ Operations with Complex Numbers ◾ Power of i ◾ Graphing Calculator and Complex Numbers

4.1 Solving Quadratic Equations

Solving Quadratic Equations by Factoring ◾ Projectiles and Gravity Models ◾ Solving Quadratic Equations by the Square Root Method ◾ Solving Quadratic Equations by Completing the Square ◾ Solving Quadratic Equations by the Quadratic Formula ◾ Quadratic Equations with Complex Solutions ◾ Nature of the Solutions of Quadratic Equations ◾ Quadratic Equations: Graphical and Numerical Solutions ◾ Summary of Solving Methods

4.2 Parabolas and Their Applications

The Vertex and Axis of Symmetry ◾ Intercepts of a Quadratic Function ◾ Sketching the Graph of a Quadratic Function ◾ The Vertex Form of a Quadratic Function ◾ Finding the Equation of a Quadratic Function ◾ Average Rate of Change

4.3 Quadratic Inequalities

Solving a Quadratic Inequality by Graphing ◾ Solving a Quadratic Inequality Algebraically ◾ Summary of Solving Methods

4.4 Other Types of Equations

Radical Equations ◾ Solving Radical Equations Algebraically ◾ Solving Radical Equations Graphically ◾ Solving Radical Equations Numerically ◾ Equations Reducible to Quadratic Form ◾ Rational Equations

4.5 Distance Formula, Midpoint Formula, and Circles

Distance Formula ◾ Midpoint Formula ◾ Circles ◾ Standard Form of the Equation of a Circle ◾ Graphing Circles ◾ General Form of the Equation of a Circle ◾ Graphing Calculator and Circles

4.6 Nonlinear Systems of Equations

Solving by Graphing ◾ Solving by Substitution ◾ Solving by Elimination ◾ Nonlinear Systems with Complex Solutions

4.7 Graphing Nonlinear Inequalities in Two Variables

Nonlinear Inequalities ◾ Graphing

Chapter 4 Summary

Chapter 4 Review

**Chapter 5 Inverse Functions and Applications**

5.0 Getting Started

Literal Equations ◾ Evaluating Functions

5.1 Finding the Inverse: Numerical, Graphical, and Symbolic Approaches

One-to-One Functions ◾ Inverse Functions ◾ Graphs of Inverse Functions ◾ Inverse Functions with Restricted Domains

5.2 Composition of Functions

Algebra of Functions ◾ Composition of Functions ◾ Composite Functions with the Graphing Calculator ◾ Decomposing Functions

5.3 Determining the Inverse Using Composition of Functions

Functions that Are Inverses of Each Other

Chapter 5 Summary

Chapter 5 Review

**Chapter 6 Exponential and Logarithmic Functions and Applications **

6.0 Getting Started

Laws of Exponents ◾ Scientific Notation

6.1 Exponential Functions and Their Graphs

Graphing Exponential Functions ◾ Transformations of Graphs of Exponential Functions ◾ Introduction to Exponential Growth and Decay ◾ Increasing or Decreasing by a Constant Percent ◾ Average Rate of Change ◾ Different Time Periods ◾ Comparing Linear and Exponential Growth

6.2 Logarithmic Functions and Their Graphs

Definition of Logarithm ◾ Evaluating Logarithms ◾ Common Logarithms ◾ Logarithmic Functions ◾ Graphing Logarithmic Functions ◾ Transformations of Graphs of Logarithmic Functions ◾ Some Applications of Logarithmic Functions

6.3 The Natural Exponential and Logarithmic Functions

The Natural Exponential Function ◾ The Natural Logarithmic Function ◾ Basic Properties of Natural Logarithms ◾ Graphs of Natural Logarithmic Functions

6.4 Exponential and Logarithmic Equations

Solving Exponential Equations with the Exponential Equality Property ◾ Solving Exponential Equations with Base 10 or Base e ◾ Solving Exponential Equations Graphically and Numerically ◾ Fundamental Properties of Logarithms ◾ Solving Exponential Equations Using Properties of Logarithms ◾ Solving Logarithmic Equations ◾ Solving Literal Equations Involving Exponential and Logarithmic Equations ◾ Change of Base Formula

6.5 Additional Exponential and Logarithmic Models

Compound Interest and Present Value ◾ Continuous Compounding and Present Value ◾ Doubling Time ◾ Annuities ◾ Amortization ◾ Logistic Function ◾ Carbon-14 Dating

Chapter 6 Summary

Chapter 6 Review

**Chapter 7 Polynomial and Rational Functions with Applications**

7.0 Getting Started

Factoring the Sum or Difference of Two Cubes ◾ Simplifying Rational Expressions

7.1 Polynomial Functions and Their Graphs

Graphs of Polynomial Functions ◾ Zeros (x-intercepts) of Polynomial Functions ◾ Properties of Polynomial Graphs ◾ Finding a Polynomial Function Given Its Graph ◾ Division of Polynomials ◾ Synthetic Division ◾ The Remainder Theorem

7.2 Rational Functions and Their Graphs

Graphs of Rational Functions and Asymptotes ◾ Using Transformations to Sketch the Graph of a Rational Function ◾ Sketching the Graph of a Rational Function ◾ Holes in Graphs of Rational Functions ◾ Finding a Rational Function Given Its Graph

7.3 Solving Polynomial and Rational Inequalities

Polynomial Inequalities ◾ Solving by Graphing ◾ Solving Algebraically ◾ Rational Inequalities ◾ Solving Rational Inequalities by Graphing ◾ Solving Rational Inequalities Algebraically

7.4 Variation

Direct Variation ◾ Inverse Variation ◾ Joint Variation ◾ Combined Variation

Chapter 7 Summary

Chapter 7 Review

**Index**

**Gisela Acosta**

Gisela Acosta holds a Bachelor of Arts, Master of Arts, and Ed.D. with majors in Curriculum, Music, and Mathematics from the University of Puerto Rico. Her doctorate degree dissertation in Mathematics Curriculum and perfect GPA earned her the UPR President’s Award for Academic Excellence. Dr. Acosta has received numerous awards for Excellency as a Mathematics Professor, and as Chair of the Department of Mathematics and Natural Sciences at the Inter American University of PR. Other awards include the NISOD Excellence in Learning Leadership Award, Distinguished Educator by the Phi Delta Kappa Honorary Society of Education, Excellency as Project Director for Title II and Title III Grants, Department of Education Special award for outstanding leadership as Consultant for the Development and Implementation of “Centers for Research in Mathematics Education,” and many other recognitions.

Dr. Acosta’s career as a Math Professor includes 21 years at the Inter American University of PR, and Valencia College, in Orlando, FL, where she has been a math professor since 1996. She has taught a wide variety of mathematics courses, from the developmental levels to advanced calculus and other advanced math courses. She has presented numerous workshops and conferences on mathematics and authored and co-authored other math publications. Dr. Acosta dedicates this second edition to Luis, her loving husband in Heaven (1944-2020).

**Margie Karwowski**

Margie Fernandez-Karwowski earned a Bachelor of Science and Master of Science in Applied Mathematics from the University of Akron and University of Central Florida, respectively. Her career in the teaching profession encompasses 20 years as a tutor, teacher, and professor at the high school, college, and university levels. Professor Karwowski’s career began at the Pre-Algebra level when she fi rst entered college. With hard work, effort, devotion, and motivated by challenge, she set her mind to pursue a career in the field of mathematics.

In 1983, fresh out of high school, Professor Karwowski backpacked throughout Western and Eastern Europe, experiencing other cultures for one month. From 1996 through 1999 she lived in Warsaw, Wiesbaden, and Budapest with her 2 children, which provided her a better appreciation of history and the world around her. These experiences helped the authors realize the need to incorporate a wide variety of subjects and topics into the mathematics classroom, which serves such a diverse student population. While living in Europe, Professor Karwowski participated in fundraisers for local orphanages which included writing a cookbook that featured international cuisine, with funds going to a home for children with AIDS. Professor Karwowski and her husband stay busy with their 5 kids and 2 grandchildren, and continue to volunteer helping the homeless and the elderly.