Khan Academy
Khan Academy: Increasing and Decreasing Intervals
Highlight intervals on the domain of a function where it's only increasing or only decreasing. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Analyze Math
Analyze Math: Differentiation of Hyperbolic Functions
Students learn about differentiation of hyperbolic functions. The tutorial consists of examples with detailed solutions.
Lawrence Hall of Science
The Math Page: An Approach to Calculus: Continuous Versus Discrete
Here is a site that clearly and thoroughly explains the the notion that calculus is the study of continuity. This page is mostly discussion of the difference between a continuous quantity and a discrete quantity. Point this site out to...
Lawrence Hall of Science
The Math Page: Topics in Pre Calculus: Functions
Here is a site that clearly and thoroughly explains functions and function notation. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to students who have...
University of Illinois
University of Illinois: Exponential Review
This site from the University of Illinois shows several basic graphs, gives properties of exponential functions, and has practice problems at the end of the site.
Cool Math
Coolmath: Solving for Time and Rates
Explanation and examples of solving exponential equations for time and rate.
Math Planet
Math Planet: Algebra 1: Exponential Growth Functions
An exponential function is a nonlinear function that has the form of y=a*b^x, where a != 0, b > 0. An exponential function with a > 0 and b > 1, like the one above, represents an exponential growth and the graph of an...
Paul Dawkins
Paul's Online Notes: Exponential and Logarithm Equations Practice Problems
In this section we will discuss various methods for solving equations that involve exponential functions or logarithm functions.
Paul Dawkins
Paul's Online Notes: Logarithmic Functions Practice Problems
In this section we will discuss logarithm functions, evaluation of logarithms and their properties. We will discuss many of the basic manipulations of logarithms that commonly occur in Calculus (and higher) classes. Included is a...
Paul Dawkins
Paul's Online Notes: Common Graphs Practice Problems
In this section we will do a very quick review of many of the most common functions and their graphs that typically show up in a Calculus class.
Cool Math
Coolmath: Continuous Compounding
Check out this example of a continuous compounding formula.
Lawrence Hall of Science
The Math Page: An Approach to Calculus: Derivatives of Logarithmic and Exponential Functions
Here is a site that clearly and thoroughly explains how to find the derivative of exponential and logarithmic functions. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point...
Lawrence Hall of Science
The Math Page: An Approach to Calculus: The Derivative
Here is a site that clearly and thoroughly explains the concept of derivative from the definition. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to...
Illustrative Mathematics
Illustrative Mathematics: F Le in the Billions and Exponential Modeling
For this task, young scholars examine world population data from 1804 to 2012 and investigate whether an exponential function is appropriate for modeling the relationship between the world population and the year. Aligns with F-LE.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Le Carbon 14 Dating, Variation 2
In this task on exponential decay, students calculate what the amount of Carbon 14 left in a preserved plant will be as time passes and when one microgram will be all that is left. Aligns with F-LE.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Le Linear or Exponential?
In this task, young scholars are asked to identify whether changes are linear or exponential. Aligns with F-LE.A.1.
Illustrative Mathematics
Illustrative Mathematics: F Le Illegal Fish
In this task, students learn about exponential functions when they investigate the exponential growth of an invasive fish population. Aligns with F-LE.B.5 and F-LE.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Le Us Population 1790 1860
In this task, students are shown a table of U.S. population data between 1790 and 1860 and are asked to explore whether exponential functions would be appropriate to model relationships within the data. The purpose of the task is to help...
Illustrative Mathematics
Illustrative Mathematics: F Le Comparing Exponentials
In this task, students work with exponential functions in a real-world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve...
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Functions
Students are shown the intersecting graphs of two exponential functions in the format of f(x) = a times b to the power of x, and are asked to explore their characteristics. They discover that the value of each function will increase by a...
Illustrative Mathematics
Illustrative Mathematics: F Le Identifying Functions
In this task, young scholars are shown a table with linear, quadratic, and exponential functions at various values of x and are asked to match the function type to each data set and explain their reasoning. Aligns with F-LE.A.1.b and...
Illustrative Mathematics
Illustrative Mathematics: F Le in the Billions and Linear Modeling
In this task, students are shown a table of world population data and asked to explore whether linear functions would be appropriate to model relationships within the data. Aligns with F-LE.A.1.b.
Illustrative Mathematics
Illustrative Mathematics: F Le Basketball Rebounds
The purpose of this task is to introduce students to an exponential decay function in the form f(x) = abx, with a concrete interpretation of the decay factor b. A table shows the rebound height of a basketball for each successive bounce....
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Growth Versus Linear Growth Ii
In this task, students compare exponential and linear functions and find that exponential functions with a base larger than one eventually exceed in value any given linear (or polynomial) function if the value of the input is...