MR. BISHOP'S MATH RESOURCES
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  • Integrated Math 3
    • Homework Calendars
    • Chapter 2 - Linear Equations, Inequalities, and Functions >
      • 2-1/2-2 Solving Equations/Inequalities
      • 2-3 Linear Functions and Slope-Intercept Form
      • 2-4 Families of Functions
      • 2-5 Absolute Value Functions and Graphs
      • 2-6 Two-Variable Inequalities
      • 2-7 Solving Systems of Equations
      • 2-8 Systems of Inequalities
      • 2-9 Systems With Three Variables
      • Chapter 2 Reviews
    • Chapter 3 - Quadratic Functions and Equations >
      • 3-1 Quadratic Functions and Transformations
      • 3-2 Standard Form of a Quadratic Function
      • 3-3 Factoring Quadratic Expressions
      • 3-3b Intercept Form
      • 3-4 Quadratic Equations
      • Graphing Quadratics Handouts
      • 3-5 Completing the Square
      • 3-6 The Quadratic Formula
      • Chapter 3 Reviews
    • Chapter 4 Polynomials and Polynomial Functions >
      • 4-1 Polynomial Functions
      • 4-2 Adding, Subtracting, and Multiplying Polynomials
      • 4-3 Polynomials, Linear Factors, and Zeros
      • 4-4 Solving Polynomial Equations
      • 4-5 Dividing Polynomials
      • 4-6 Theorems About Roots of Polynomial Equations
      • Chapter 4 Handouts
      • Chapter 4 Reviews
    • Chapter 5 - Rational Expressions and Functions >
      • 5-1 Simplifying Rational Expressions
      • 5-2 Multiplying and Dividing Rational Expressions
      • 5-3 Adding and Subtracting Rational Expressions
      • 5-5 The Reciprocal Function Family
      • 5-7 Solving Rational Equations
      • Chapter 5 Handouts
      • Chapter 5 Reviews
    • Chapter 6 - Radical Expressions and Functions >
      • 6-1 Roots and Radical Expressions
      • 6-2 Multiplying and Dividing Radical Expressions
      • 6-3 Binomial Radical Expressions
      • 6-4 Rational Exponents
      • 6-5 Solving Square Root and Other Radical Equations
      • 6-6 Functions Operations
      • 6-7 Inverse Relations and Functions
      • 6-8 Graphing Radical Functions
      • Chapter 6 Handouts
      • Chapter 6 Reviews
    • Chapter 7 - Exponential and Logarithmic Functions >
      • 7-1 Exploring Exponential Models
      • 7-2 Properties of Exponential Functions
      • 7-3 Logarithmic Functions as Inverses
      • 7-4 Properties of Logarithms
      • 7-5 Exponential and Logarithmic Equations
      • 7-6 Natural Logarithms
      • Chapter 7 Handouts
      • Chapter 7 Reviews
    • Chapter 8 - Trigonometric Functions >
      • 8-0 Right Triangle Trigonometry
      • 8-1 Exploring Periodic Data
      • 8-2 Angles and the Unit Circle
      • 8-3 Radian Measure
      • Chapter 8 Handouts
      • Chapter 8 Reviews
    • Spring 2019 Final Project
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Chapter 7 - Differential Equations
​and Mathematical Modeling

7.1 - Slope Fields and Euler's Method
7.2 - Antidifferentiation by Substitution
7.4- Exponential Growth and Decay
Chapter 7 Reviews

One of the early accomplishments of calculus was predicting the future position of a planet from its present position and velocity.  Today this is just one of many situations in which we deduce everything we need to know about a function from one of its known values and its rate of change.  From this kind of information, we can tell how long a sample of radioactive polonium will last; whether, given current trends, a population will grow or become extinct; and how large major league baseball salaries are likely to be in the year 2020.  In this chapter, we examine the analytic, graphical, and numerical techniques on which such predictions are based.  (Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook Calculus - Graphical, Numerical, Algebraic.)


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  • Home
  • Integrated Math 3
    • Homework Calendars
    • Chapter 2 - Linear Equations, Inequalities, and Functions >
      • 2-1/2-2 Solving Equations/Inequalities
      • 2-3 Linear Functions and Slope-Intercept Form
      • 2-4 Families of Functions
      • 2-5 Absolute Value Functions and Graphs
      • 2-6 Two-Variable Inequalities
      • 2-7 Solving Systems of Equations
      • 2-8 Systems of Inequalities
      • 2-9 Systems With Three Variables
      • Chapter 2 Reviews
    • Chapter 3 - Quadratic Functions and Equations >
      • 3-1 Quadratic Functions and Transformations
      • 3-2 Standard Form of a Quadratic Function
      • 3-3 Factoring Quadratic Expressions
      • 3-3b Intercept Form
      • 3-4 Quadratic Equations
      • Graphing Quadratics Handouts
      • 3-5 Completing the Square
      • 3-6 The Quadratic Formula
      • Chapter 3 Reviews
    • Chapter 4 Polynomials and Polynomial Functions >
      • 4-1 Polynomial Functions
      • 4-2 Adding, Subtracting, and Multiplying Polynomials
      • 4-3 Polynomials, Linear Factors, and Zeros
      • 4-4 Solving Polynomial Equations
      • 4-5 Dividing Polynomials
      • 4-6 Theorems About Roots of Polynomial Equations
      • Chapter 4 Handouts
      • Chapter 4 Reviews
    • Chapter 5 - Rational Expressions and Functions >
      • 5-1 Simplifying Rational Expressions
      • 5-2 Multiplying and Dividing Rational Expressions
      • 5-3 Adding and Subtracting Rational Expressions
      • 5-5 The Reciprocal Function Family
      • 5-7 Solving Rational Equations
      • Chapter 5 Handouts
      • Chapter 5 Reviews
    • Chapter 6 - Radical Expressions and Functions >
      • 6-1 Roots and Radical Expressions
      • 6-2 Multiplying and Dividing Radical Expressions
      • 6-3 Binomial Radical Expressions
      • 6-4 Rational Exponents
      • 6-5 Solving Square Root and Other Radical Equations
      • 6-6 Functions Operations
      • 6-7 Inverse Relations and Functions
      • 6-8 Graphing Radical Functions
      • Chapter 6 Handouts
      • Chapter 6 Reviews
    • Chapter 7 - Exponential and Logarithmic Functions >
      • 7-1 Exploring Exponential Models
      • 7-2 Properties of Exponential Functions
      • 7-3 Logarithmic Functions as Inverses
      • 7-4 Properties of Logarithms
      • 7-5 Exponential and Logarithmic Equations
      • 7-6 Natural Logarithms
      • Chapter 7 Handouts
      • Chapter 7 Reviews
    • Chapter 8 - Trigonometric Functions >
      • 8-0 Right Triangle Trigonometry
      • 8-1 Exploring Periodic Data
      • 8-2 Angles and the Unit Circle
      • 8-3 Radian Measure
      • Chapter 8 Handouts
      • Chapter 8 Reviews
    • Spring 2019 Final Project
  • About
  • Contact