UTPA STEM/CBI Courses/Algebra/Exponential Growth Regression

Course Title: College Algebra

Lecture Topic: Exponential Growth Regression

Instructor: Cesar Santos

Institution: Laredo Community College

Backwards Design

Course Objectives

• Primary Objectives- By the next class period students will be able to:
  • Use exponential growth regression to model real-life problems.

• Sub Objectives- The objectives will require that students be able to:
  • Determine an exponential regression model equation to represent the data.
  • Graph an exponential regression model equation on the set data points.
  • Decide whether the exponential regression model equation is a “good fit.”

• Difficulties- Students may have difficulty:
  • Identifying the variables and the values for x- and y- given a data set.
  • Setting up real-world application problems involving Exponential Regression.
  • Performing appropriate operations in order to graph the data using Stat Plot, Correlation, and Exponential Regression on the TI-84 calculator.
  • Evaluating exponential functions.

• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
  • If a student shows up without even knowing they were infected with the Ebola Virus, how many days would it take to get the whole class infected?

Model of Knowledge

• Concept Map
  • Graphing data (Stat Plot) given a data set.
  • Exponential Regression given a data set.
  • Evaluating Exponential Regression functions

• Content Priorities
  • Enduring Understanding
    • Graphing data points that deal with an exponential regression (Stat Plot).
    • Perform the exponential regression and graph the exponential regression function on the calculator.
  • Important to Do and Know
    • Family of functions: exponential growth and exponential decay functions.
    • Properties of exponents.
    • Transformation of functions with emphasis on exponential functions.
  • Worth Being Familiar with
    • Basic knowledge on how to use the TI-84 calculator (example: how to graph functions).
    • Perform other types of regression (linear, quadratic) on given a data set.

Assessment of Learning

• Formative Assessment
  • In Class (groups)
    • Given a word problem, students will create a table of values given certain assumptions.
    • Use the calculator to create a graph by plotting points (Stat Plot)
    • Use the calculator to find the exponential regression function.
    • Graph the exponential regression function on the given points to see if indeed there is a “good fit.”
• Summative Assessment
  • In groups, group leaders go public on what it means to deal with infectious disease in a hospital.
  • Activity 5 Handout: Infectious Disease: The Zombie Strain.

Legacy Cycle

OBJECTIVE

By the next class period, students will be able to:

• Use exponential growth regression to model real-life problems.

The objectives will require that students be able to:

• Determine an exponential regression model equation to represent the data.
• Graph an exponential regression model equation on the set data points.
• Decide whether the exponential regression model equation is a “good fit.”

THE CHALLENGE

If a student shows up without even knowing they were infected with the Ebola Virus, how many days would it take to get the whole class infected?

GENERATE IDEAS

By clearing up some assumptions, as a class we will create a table based on the trend of infections. Once we have the table, we graph the points, and derive an equation from the data using exponential regression.

MULTIPLE PERSPECTIVES

The students work in small groups for 10-20 minutes and answer some questions on their case study.

RESEARCH & REVISE

The teacher introduces a method to plot points (Stat plot) on the graphing calculator. The students will also be shown how to perform the exponential regression on the calculator given a table of values. The students will then determine if the function is a “good fit” by graphing the function.

TEST YOUR METTLE

Each group will get a case study. Based on the data, they will answer questions about the infectious disease the hospital is dealing with.

GO PUBLIC

One student (group leader) shows what disease is the hospital is dealing with given their perspective case study.

Pre-Lesson Quiz

Various material can be tested here, depending on time constraints.

Test Your Mettle Quiz

Various material can be tested here, depending on time constraints.