--- title: Exponential Functions description: Exponential functions are mathematical functions where a constant base is raised to a variable exponent. Learners will understand growth and decay models, Euler's number, and graphing techniques, enabling them to analyze population growth and financial interest. category: mathematics subcategory: algebra difficulty: beginner, intermediate, advanced url: /subject/exponential-functions --- # Exponential Functions Exponential functions are mathematical functions where a constant base is raised to a variable exponent. Learners will understand growth and decay models, Euler's number, and graphing techniques, enabling them to analyze population growth and financial interest. ## Available Resources 1 Books • 3 Courses • 3 Websites ## Courses ### 1. Exponential growth & decay Master exponential growth & decay with this course by Sal Khan! Explore exponential functions and real-world applications. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay **Tags:** exponential-growth, exponential-decay, exponential-functions, algebra ### 2. Introducción al cálculo **Author:** Jaume Pujol, Mercè Villanueva Spanish-language course from the Universitat Autònoma de Barcelona that reviews numbers and functions, polynomial, exponential, logarithmic and trigonometric functions, then introduces differentiation, integration and complex numbers. Prepares students for a first-semester university calculus course in science or engineering. **Difficulty:** Beginner | **Language:** English | **Duration:** 6-8 horas de trabajo por módulo | **Price:** Free **Link:** https://www.coursera.org/learn/introduccion-al-calculo **Tags:** precalculus, functions, trigonometry, differentiation, integration, spanish-language ### 3. Algebra: Elementary to Advanced - Polynomials and Roots **Author:** Joseph W. Cutrone Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/polynomials-roots **Tags:** polynomials, factoring, exponents, radicals, algebra ## Books ### 1. e: The Story of a Number **Author:** Eli Maor History of e from Napier's logarithms through Newton, Bernoulli and Euler, tracing how compound interest, the area under a hyperbola and the shape of a hanging chain all converge on the same constant. Light calculus in optional sections. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0691168482?tag=edmonddante07-20 **Tags:** euler-number, exponential-functions, logarithms, history-of-mathematics, calculus ## Youtubes ### 1. Exponential growth and epidemics **Author:** Grant Sanderson Nine-minute treatment of why constant proportional growth produces the curve it does, using early 2020 case counts as the running dataset, then showing where the logistic ceiling bends an exponential back down. No calculus prerequisite. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.youtube.com/watch?v=Kas0tIxDvrg **Tags:** exponential-growth, logistic-growth, epidemiology, mathematical-modeling ### 2. What's so special about Euler's number e? (Essence of Calculus, Ch. 5) **Author:** Grant Sanderson Grant Sanderson shows why every exponential function is proportional to its own derivative, and why e is the unique base where that proportionality constant equals one. Animated throughout; assumes familiarity with derivatives. e is not a number you memorize, it is the base at which a growth curve equals its own rate of growth. This is the mental model that makes every later appearance of e (finance, decay, differential equations) feel inevitable rather than arbitrary. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.youtube.com/watch?v=m2MIpDrF7Es **Tags:** euler-number, exponential-functions, derivatives, calculus ## Websites ### 1. OpenStax College Algebra 2e — Ch. 6: Exponential and Logarithmic Functions **Author:** Jay Abramson Chapter 6 of Jay Abramson's peer-reviewed OpenStax textbook: exponential functions, graphing and transformations, e and continuous compounding, models for growth and decay, and fitting exponential curves to data, with worked examples and answer-keyed exercises. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://openstax.org/books/college-algebra-2e/pages/6-introduction-to-exponential-and-logarithmic-functions **Tags:** exponential-functions, logarithms, college-algebra, exponential-models, continuous-compounding ### 2. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 3. mathsisfun.com MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathsisfun.com **Tags:** websites, mathematics-statistics, algebra --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/exponential-functions