Lesson+1+Outline

** Bellringer/Brain Teaser: ** On webpage, [|__http://www.mathwarehouse.com/algebra/linear_equation/linear-equation-interactive-activity.php__] , have several linear equations with directions: Write a table with x values from -5 to 5. Find the y values. Also find the slope of each function. Then discuss how to find x-intercepts, y-intercepts and the slope of linear functions. This should be a complete review for students.
 * (Lesson used in a 1-1 classroom) **

** Break Class into Groups ** - chosen by teacher based on learning styles and level of understanding ( Cooperative Learning ) and have them discuss the following handout, which they students will access on the teacher webpage. Students will also be assigned roles below.

** GROUP ROLES: ** __Director:__ You will be the reader for your group. You will explain instructions to the group. You will also make sure that the group is on task at ALL times. __Record Checker:__ You will make sure everyone in the group is filling out their toolkit (notes) as you work through the investigations. You will encourage your group to take detailed notes. __Verifier:__ You will make sure everyone in the group is working at the same pace. You will also make sure everyone in the group understands the concepts and conclusions. __Quality Controller:__ You will observe investigations or experiments to determine the accuracy of data collected. You will make sure everyone in your group has compared/checked their answers. You and you alone are allowed to visit other groups if you need a push in the right direction.

** What is an exponential function? **
An exponential function has an exponent that contains a variable and whose base is any positive number except one. Generally, the form of an exponential function is y =ab x, where a ≠ 0, b > 0, and b ≠ 0. Remember that not all functions that involve an exponent are exponential functions. For example, y = x 2 or y = 2x 3 + x 2 + 4x –4 are not exponential functions. Some examples of exponential functions are y = 2 x, y = 3 (x+1) , and y = 6(1.05) 2x. Consider the three exponential functions f(x) = 3 x, g(x) = .5(2) x and h(x) = 12(1/2) x. Plug all three of these functions in your calculator and compare the graphs and the table.

** What are some important characteristics of exponential curves? **
There are many real-world examples of exponential functions of the form y = ab x. If b > 1, the exponential function represents a growth model. Examples include compound interest, population growth, and the national debt. If 0 < b < 1, the exponential function represents a decay model. Examples include radioactive decay, depreciation (the loss or decline of value), and population decline. Now that you know what an exponential function is, and some of its possible applications, consider the graph bel [|ow.]



Note that exponential functions y = ab x have graphs with continuous curves that approach but never cross a horizontal asymptote. The graphs have a y-intercept equal to the a value in their equation but no x-intercept. They are either increasing or decreasing and the y-values are all positive. Does it have a rate of change or a slope? This is the question you will investigate in this Web Inquiry.

** Independent Practice: WebQuest ( Project Based Learning)  ** ** [|__http://www.otherwise.com/population/index.html__] ** ** [|__http://www.learner.org/courses/learningmath/algebra/session7/part_b/index.html__] **
 * Read the first three paragraphs. Answer questions 6-11 on the [|Questions] sheet.
 * Open the Exponential Growth web page and read directions for using the applet as well as descriptions of two experiments.
 * Open the provided applet to simulate each experiment and to answer questions 10 and 11.
 * ** // Quickly review the two salary plans. Answer question 12. // **
 * ** // Scroll to the bottom of the page to click on the Play Video button. // **
 * ** // Listen for the words used to describe rate of change for both linear and exponential functions. // **

Submit your web quest Questions sheet via email.