Exponential Growth and Decay (UMAP)

This unit reviews exponents and introduces the notions of doubling time and half-life. Students, given a table of data or graph showing the doubling period (half-life) of a quantity, should be able to a) state the length of the doubling period or half-life; b) use the concept of half-life or doubling period to fill in missing points; c) recognize a given function as exponential by its constant doubling period or half-life; d) write formulas that fit that data using an exponential function to the base 2 or to the base 1/2.

Table of Contents:

1. INTRODUCTION

2. REVIEW OF EXPONENTS

3. POPULATION GROWTH AND DOUBLING TIMES
3.1 Computation of a Doubling Period Given Annual Percentage Growth
3.2 Computation of Doubling Period from Graph of an Exponential Function

4. FORMULA FOR EXPONENTIAL GROWTH
4.1 Formula for Growth of a Population
4.2 Formula for Growth of a Bank Account

5. HALF-LIVES
5.1 Half-Life of the Charge in a Capacitor
5.2 Half-Life of Radioactive Carbon
5.3 Formula for Expressing Exponential Decay

6. ANSWERS TO EXERCISES

7. MODEL EXAM

8. ANSWERS TO MODEL EXAM