Exponential Growth & Decay

This module will provide students with a foundation for understanding exponential growth, especially as contrasted with linear growth. Many skills are included because they provide opportunities for students to increase their understanding of exponential growth. For example, the geometric average is introduced, not so much because it is a vital skill to know, but because it provides another opportunity to show how exponential growth really is different than linear growth. Students learn to contrast exponential thinking with linear thinking. Lesson 1 Patterns of Growth Students contrast linear (common difference) with exponential (common ratio) growth, by examining data. Lesson 2 Representing Patterns of Growth By examining data sets, graphs, words, and symbols students compare and contrast linear and exponential growth. Nitty Gritty: Linear Functions. Lesson 3 Doubling Students have a strong common sense and intuition about doubling and halving. The intuitive ideas of doubling and halving are formalized. Lesson 4 Doubling Variations Students will extend the doubling formula to allow for different time periods and work with the properties of exponents. This lesson deals exclusively with the symbolic form. Lesson 5 Beyond Doubling In this lesson, the base of the doubling formula will be extended to include other bases. Lesson 6 Relating Different Bases Students learn how percent growth relates to the extended doubling formula. This lesson brings the symbolic representation to closure, showing the effects of the different parameters in y = a·b(x/n). Lesson 7 Overpopulation In this lesson, students make exponential models of world population data, using concepts of Lessons 1-6. This also sets up Lessons 11, 12 and 13. Lesson 8 A Look at Logs. This lesson introduces properties and definition of logarithms and the relationship of these ideas to exponents. Lesson 9 A Sense for Logarithms Students explore decibels to see how logs are used and interpreted. Solving exponential equations is a part of this in-depth look at an application of logarithms. Lesson 10 Life in a Petri Dish Students apply their knowledge to do log transformation of data and to plot semi-log graphs. Lesson 11 Land and Its Limits (Optional) This lesson is an application on the issues of overpopulation. It can be done in class or as individual project. Lesson 12 Resources and Limits (Optional) This lesson is an application on the issues of overpopulation. It can be done in class or as individual project. Lesson 13 The Sky is Falling (Optional) This lesson is an application on the issues of overpopulation. It can be done in class or as individual project. Compare this module to traditional course topics in the Matrix of Course Competencies. If one of the lessons has a link, you can preview that lesson. Other modules: Beat Ratios Functions Exp. Growth Data & Graphs Representing Data Finance Geometry Sampling Non-linear Behavior Linear Behavior Sets and Logic Patterns Probability Systems Right Tri. Trig.