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

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