About This Chapter
Calculus Applications: Rate of Change - Chapter Summary
This informative chapter presents rate of change as it's used in calculus. Lessons cover how the rate of change of a function is determined and the formula used to find the instantaneous rate of change in a function. Once you complete this chapter, you should be able to:
- Tell the difference between exponential growth and decay
- Calculate both exponential growth and decay
- Graph logistic population growth
You can understand even the most challenging topics with help from our professionally-designed learning materials. It's easy to go back or jump ahead in any video lesson using the video tabs feature in the timeline. Each lesson is followed by a short multiple-choice quiz that makes a great test prep tool ahead of an exam. If at any time you need assistance, feel free to reach out to one of our instructors for help.
1. Determine the Rate of Change of a Function
In this lesson, we will learn about the rate of change of a function with specific focus on linear and exponential functions while examining the graphs of both types of functions.
2. Finding Instantaneous Rate of Change of a Function: Formula & Examples
In this lesson, you will learn about the instantaneous rate of change of a function, or derivative, and how to find one using the concept of limits from Calculus.
3. Exponential Growth vs. Decay
How is it that it only takes four years for our computer to go from top-of-the-line to almost worthless? Well, it has something to do with what's called exponential decay, which we'll learn about here!
4. Calculating Rate and Exponential Growth: The Population Dynamics Problem
You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.
5. Logistic Population Growth: Equation, Definition & Graph
Populations tend to get larger until there is no longer enough food or space to support so many individuals. This type of growth is called logistic population growth, and you can learn more about it in this lesson.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards