Illustrative Mathematics
Illustrative Mathematics: F Le Linear or Exponential?
In this task, students 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 Bacteria Populations
This task provides a real-world context for interpreting and solving exponential equations. Students are asked to examine the equations representing the growth of three colonies of the bacterium that causes pneumonia, each colony being...
Illustrative Mathematics
Illustrative Mathematics: F Le Carbon 14 Dating
The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating. Aligns with F-LE.A.4.
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...
Illustrative Mathematics
Illustrative Mathematics: F Le Two Points Determine an Exponential Function Ii
In this task, learners are shown a graph of an exponential equation, with two points labeled with their coordinates, and are asked to find the values of a and b in the equation. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le Two Points Determine an Exponential Function I
This is a simple task where students are shown a graph of an exponential equation, with two points labeled with their coordinates, and are asked to find the values of a and b in the equation. Aligns with F-LE.A.2.
Illustrative Mathematics
Illustrative Mathematics: F Le What Functions Do Two Graph Points Determine?
In this task, students find a unique linear function, a unique exponential function, and more than one quadratic function that go through the same two points on the coordinate grid. Aligns with F-LE.A.
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, young scholars 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.
CK-12 Foundation
Ck 12: Analysis: Graphs of Polynomials Using Zeros
[Free Registration/Login may be required to access all resource tools.] In this lesson students use ''X'' and ''Y'' intercepts to graph polynomials of 3rd degree or higher. Students examine guided notes, review guided practice, watch...
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 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 Functions From Tables & Graphs
Write exponential functions of the basic form f(x)=a * b squared, either when given a table with two input-output pairs, or when given the graph of the function. 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: 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...