Chapter 2 - Models of Growth: Rates of Change
- Index
-
About this Chapter
- Section 2.1 Rates
of Change
- 2.1.1 Average Rates of Change: Slopes of Linear Equations
- 2.1.2 Average Rates of Change for More General Functions
- 2.1.3 Mathematical Notation: The Difference Quotient
- Section Summary
- Exercises
- Problems
- Section 2.2 The Derivative: Instantaneous Rates of Change
- 2.2.1 Zooming In: Local Linearity
- 2.2.2 Graphical Calculation of Rates of Change
- 2.2.3 Algebraic Calculation of Rates of Change
- 2.2.4 The Derivative
- 2.2.5 Notation and Terminology
- Section Summary
- Exercises
- Problems
- Section 2.3 Symbolic Calculation of Derivatives
- 2.3.1 Derivatives of Power Functions: Initial Cases
- 2.3.2 Derivatives of Power Functions: General Rules
- Section Summary
- Exercises
- Problems
- Section 2.4 Exponential Functions
- 2.4.1 Interest Rates and Exponential Growth
- 2.4.2 Derivatives of Exponential Functions
- 2.4.3 The
Natural Base
- 2.4.4 Derivatives
of More General Exponential Functions
- 2.4.5 Symbolic
Derivatives of Exponential Functions: Other Bases
- Section Summary
- Exercises
- Problems
- Section 2.5 Modeling Population Growth
- 2.5.1 A Difference Equation and a Differential Equation
- 2.5.2 Solutions of the Differential Equation
- 2.5.3 Slope Fields
- 2.5.4 Differential-Equation-with-Initial-Value Problems
- Section Summary
- Exercises
- Problems
- Section 2.6 Logarithms and Representation of Data
- 2.6.1 Logarithmic Plots of Data: Natural Base
- 2.6.2 Logarithmic Plots of Data: Base 10
- 2.6.3 Power Functions and Log-Log Plotting
- 2.6.4 Finding a Power Model
- Section Summary
- Exercises
- Problems
- Chapter Summary
- Chapter Review
- Concepts and Applications
- Formulas
- Project 1: The Early Spread of AIDS in the US
- Project 2: Building a Box (printer required)