Illustrative Mathematics
Illustrative Mathematics: F Le Algae Blooms
This problem examines the growth of algal blooms in Chesapeake Bay. Students build an exponential function modeling algae concentration based on the information provided, and gain an appreciation for the exponential growth exhibited...
Illustrative Mathematics
Illustrative Mathematics: F Le a Saturating Exponential
For this problem, students use an exponential equation to investigate the warming up of a cold beverage on a summer day and analyze a graph to estimate temperatures. Aligns with F-LE.B.5 and F-BF.B.
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Growth Versus Polynomial Growth
In this problem, students compare the growth of exponential functions versus polynomial functions and find that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large. Aligns...
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Growth Versus Linear Growth I
In this task, students analyze two methods of payment to discover how an exponentially increasing quantity eventually surpasses a linearly increasing quantity. Aligns with F-LE.A.3.
Illustrative Mathematics
Illustrative Mathematics: F Le Equal Factors Over Equal Intervals
For this task, students investigate the changes that take place in the values of a function to determine that exponential functions grow by equal factors over equal intervals. Aligns with F-LE.A.1.a.
Illustrative Mathematics
Illustrative Mathematics: F Le Linear Functions
In this problem, students are presented with the equations of two linear functions and their intersecting graphs. They are asked to label the graphs and compute values for several points on the graphs. Aligns with F-LE.A.1.b.
Lawrence Hall of Science
The Math Page: An Approach to Calculus: Evaluating E
Here is a site that clearly and thoroughly explains the limit definition of the transcendental number e. There are several different approaches used to find the value. Point this site out to students who have been absent or who need...
University of California
Ucla Mathematics Department:average Value of a Function
UCLA Mathematics Department provides specific example of the average value of a function.
Khan Academy
Khan Academy: Graphing Exponential Growth & Decay
Graph exponential functions. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Algebra Ii: Graphs of Rational Functions
Determine which of four graphs fits the formula of a given function. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Algebra I: Exponential vs. Linear Growth Over Time
Practice analyzing the end behavior of two functions that model similar real-world relationships, where one function is exponential and the other is polynomial. Students receive immediate feedback and have the opportunity to try...
Khan Academy
Khan Academy: Algebra I: Exponential vs. Linear Models
Given a description of a real-world relationship, determine whether that relationship is linear or exponential. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Algebra I: Linear vs. Exponential Growth: From Data
Given a table with values of two quantities over time, determine whether the quantities grow linearly or exponentially. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive...
Khan Academy
Khan Academy: Average Rate of Change: Graphs and Tables
Find a function's average rate of change over a specific interval, given the function's graph or a table of values. Students receive immediate feedback and have the opportunity to try questions repeatedly or receive hints.
Khan Academy
Khan Academy: Average Rate of Change Word Problems
Find and represent the average rate of change of a real-world relationship. Students receive immediate feedback and have the opportunity to try questions repeatedly or receive hints.
Khan Academy
Khan Academy: Average Rate of Change
Find the average rate of change of a function over a given interval. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Algebra I: Find Inverse Functions
Practice finding the formula of the inverse function of a given polynomial, radical, or rational function. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Algebra I: Evaluate Inverse Functions
Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or...
Khan Academy
Khan Academy: Algebra Ii: Graphs of Exponential Functions
Graph exponential functions and find the appropriate graph given the function. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Algebra I: Sequences Word Problems
Given a verbal description of a real-world relationship, determine the sequence that models that relationship. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Khan Academy
Khan Academy: Interpret Change in Exponential Models
Given a function that models an exponential situation, find the factor by which the quantity changes per unit time interval. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or...
Khan Academy
Khan Academy: Interpret Time in Exponential Models
Given a function that models an exponential situation, find the time interval over which the quantity changes by a given factor. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or...
Khan Academy
Khan Academy: Algebra Ii: Construct Exponential Models
Given a verbal description of the rate of change of a real world situation, find the exponential function that models it. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive...
Khan Academy
Khan Academy: Linear Models Word Problems
Solve general word problems about real-world relationships that can be modeled by linear equations or functions. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video, or receive hints.