Applied Mathematical Modeling and Problem Solving

Description

1 Introduction to Problem Solving and Mathematical Models

1.1 The Bookstore

1.2 The Classroom

1.3 Make Me an Offer

1.4 Proportional Reasoning and Scaling

1.5 Fuel Economy

1.6 Florida Heat

1.7 Fill ’er Up

1.8 Mathematical Modeling

1.9 Fund-Raiser Revisited

1.10 Leasing a Copier

1.11 Comparing Energy Costs

1.12 Summer Job Opportunities

1.13. Graphs Tell Stories

1.14. Heating Schedule

2 Linear Function Models and Problem Solving

2.1 How Fast Did You Lose?

2.2 The Snowy Tree Cricket

2.3 Depreciation

2.4 Skateboard Heaven

2.5 Family of Functions

2.6 Predicting Population

2.7 A New Camera

2.8 Body Fat Percentage

2.9 College Tuition

2.10 Measuring Up

2.11 Smartphone Plan Options

2.12 Modeling a Business

2.13 Healthy Lifestyle

2.14 How Long Can You Live?

2.15 Will Trees Grow?

3 Problem Solving with Quadratic and Variation Function Models

3.1 The Amazing Property of Gravity

3.2 Baseball and the Willis Tower

3.3 The Shot Put

3.4 Per Capita Personal Income

3.5 Sir Isaac Newton

3.6 Ups and Downs

3.7 Heat Index

3.8 A Thunderstorm

3.9 The Power of Power Functions

3.10 Diving Under Pressure, or Don’t Hold Your Breath

3.11 Loudness of a Sound

4 Modeling with Exponential and Logarithmic Functions

4.1 Going Shopping

4.2 Take an Additional 20% Off

4.3 Inflation

4.4 The Summer Job

4.5 National Debt

4.6 Population Growth

4.7 Bird Flu

4.8 The Diameter of Spheres

4.9 Walking Speed of Pedestrians

4.10 Walking Speed of Pedestrians, continued

4.11 The Elastic Ball

4.12 Changing Demographics

4.13 Frequency and Pitch

5 Using Geometric Models to Solve Problems

5.1 Walking around Bases, Gardens, Trusses, and Other Figures

5.2 Long-Distance Biking

5.3 Walking around, Revisited

5.4 How Big Is That Circle?

5.5 A New Pool and Other Home Improvements

5.6 How Big Is That Angle?

5.7 Not Exactly the Same

5.8 How about Pythagoras?

5.9 The Leaning Tower of Pisa

5.10 Tessellations

5.11 Painting Your Way through the Summer

5.12 Truth in Labeling

5.13 Analyzing an Ice Cream Cone

5.14 Summertime

5.15 Math in Art

6 Problem Solving with Graphical and Statistical Models

6.1 Visualizing Trends

6.2 Bald Eagle Population

6.3 People and Places

6.4 The Class Survey

6.5 Class Survey continued

6.6 A Switch Decision

6.7 What Is Normal?

6.8 Sampling a Population

6.9 Highway Proposal: Yes or No?

6.10 Statistical Survey

6.11 What’s the Cause?

7 Problem Solving with Probability Models

7.1 Chances Are!

7.2 Choices

7.3 Experimenting with Probabilities

7.4 Conditional Probabilities

7.5 Weather Forecasting

7.6 Selecting and Rearranging Things

7.7 How Many Boys (or Girls)?

8 Problem Solving with Financial Models

8.1 Income and Expenses

8.2 Banking Options

8.3 Time Is Money

8.4 Continuous Compounding

8.5 Saving for Retirement

8.6 Buy or Lease?

8.7 Home Sweet Home

8.8 Renting versus Buying a House

8.9 Buy Now, Pay Later

8.10 Insuring the Future

8.11 The Stock Market

8.12 Which Is the Best Option?

This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value–this format costs significantly less than a new textbook. Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson’s MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson’s MyLab & Mastering products.

This text provides a one-semester alternative to the traditional two-semester developmental algebra sequence for non-STEM (Science, Technology, Engineering, and Math) students. This new approach offers an accelerated pathway to college readiness through developmental math, preparing non-STEM students to move directly into liberal arts math or introductory statistics, while also preparing STEM students for intermediate algebra.

Active Learning for Active Students

In the Mathematics in Action series, students discover mathematical concepts through activities and applications that demonstrate how math applies to their everyday lives. Different from most math books, this series teaches through activities–encouraging students to learn by constructing, reflecting on, and applying the mathematical concepts. The user-friendly approach instills confidence in even the most reticent math students and shows them how to interpret data algebraically, numerically, symbolically, and graphically. The active style develops mathematical literacy and critical thinking skills. Updated examples, brand-new exercises, and a clearer presentation make the Fifth Edition of this text more relevant than ever to today’s students.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

NOTE: You are purchasing a standalone product; MyMathLab does not come packaged with this content.

About the Textbook

• Activity-based learning allows students to take an active role in their learning. By giving students the math they encountered in high school or in previous courses, but in a new and meaningful context, this text encourages student engagement and allows for a higher level of conceptual learning, while providing a solid foundation of mathematical skills.

• To complete an activity, students write directly in their books, answering questions, completing tables, and manipulating real information to develop mathematical understanding.
• The variety of activities within each chapter allows instructors to customize the text to fit the needs and interests of their students.

• Project Activities in each chapterprovide intriguing, real-data applications that help students integrate and apply the mathematical concepts they have learned, and solidify their comprehension of the material in class. They go beyond pen and paper, also requiring measurement and data collection, to give students the opportunity to explore particular skills and concepts they have learned in greater depth, either independently or in groups

• Summary Boxes of the main concepts appear at the end of each activity to help students recognize and connect critical topics and concepts.

• Review exercises offer ample opportunity for students to tie the concepts together and apply what they have learned.

• Skills Check exercises occur periodically throughout the text to provide ample practice with basic skills.
• What Have I Learned? problems at the end of each cluster require students to pull together the topics they’ve learned and reflect on recently presented concepts. This feature also prepares students for upcoming material by helping them develop a strong foundation.
• How Can I Practice? exercises at the end of each cluster are an important self-assessment tool. They show students how to apply recently covered concepts and give students a chance to practice key skills, bridging the gap between abstraction, skills, and application.
• Gateway Review exercises conclude each chapter. These exercises help students assess their understanding of the chapter concepts and then synthesize those concepts with material from previous chapters

Also available with MyMathLab^®

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

• Fully HTML5-compatible eText, media, and exercises are device-aware and can now be used on mobile devices.
• The video program provides:
• A conceptual overview of many topics to help answer the question “how will I ever use this material?”
• A walkthrough of lessons and examples at the learning outcome level.
• MyMathLab provides Learning Catalytics–an interactive, student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking. Instructors, you can:
• Pose a variety of open-ended questions that help your students develop critical thinking skills
• Monitor responses to find out where students are struggling
• Use real-time data to adjust your instructional strategy and try other ways of engaging your students during class
• Manage student interactions by automatically grouping students for discussion, teamwork, and peer-to-peer learning
• Learning Catalytics contains Pearson-created content for developmental math that allows you to take advantage of this exciting technology immediately.