Exponential functions in the Real World

 

Name:  Monica Sustaita

Title of lesson: Exponential functions in the Real World

Date of lesson:  Thursday, Week 4

Length of lesson: 1-2 days

 Description of the class:

                     Name of course:  Algebra I

                     Grade level: 8th or 9th grade

                     Honors or regular:  Regular

 

Source of the lesson:

            Miranda and the Rookie

http://mathforum.org/tpow/print_puzzler.ehtml?puzzle=207

 

TEKS addressed:

(a) Basic understandings

(4) Relationship between equations and functions. Equations arise as a way of asking and answering questions involving functional relationships. Students work in many situations to set up equations and use a variety of methods to solve these equations.

(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, numerical, algorithmic, graphical), tools, and technology, including, but not limited to, powerful and accessible hand-held calculators and computers with graphing capabilities and model mathematical situations to solve meaningful problems.

(d) Quadratic and other nonlinear functions: knowledge and skills and performance descriptions.

3) The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. Following are performance descriptions.

(A) The student uses patterns to generate the laws of exponents and applies them in problem-solving situations.

(B) The student analyzes data and represents situations involving inverse variation using concrete models, tables, graphs, or algebraic methods.

(C) The student analyzes data and represents situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods

 

I.       Overview

In this lesson, students will get to see how an exponential function works in the real world.  It is important because they can see how real life situations can be modeled by functions.

 

II.  Performance or learner outcomes

            Students will be able to:

á        Describe the effects of exponential functions

III. Resources, materials and supplies needed

á        Computer per group

á        Microsoft Excel

IV. Supplementary materials, handouts.

á        Handout and questions

 

Five-E Organization

Teacher Does                     Probing Questions                      Student Does       

Engage:

Talk a little about money and give an initial situation. 

 

Explain the question. 

 

 

 

So, which salary would you take right now, MirandaÕs or the rookieÕs?  Why?

 

Thinking a million dollars is going to be way more than double the amount from year to year, they choose MirandaÕs. 

                                                   

Explore:

Handout the problem and divide the students into groups.

 

Walks around, monitoring the progress of the groups.

 

 

Shows them how to make a graph using Excel. 

 

     

 

 

 

 

 

 

 

Describe the graphs in your group. 

Students break into groups and get into Excel.

 

 

 

Enter the data into Excel giving titles where needed. 

 

 

See and compare the graphs.

    

Explain:

As a class, we come together and answer the questions.

 

 

 

 

 

 

What is MirandaÕs salary in year 15?  What is the rookieÕs?

 

In which year does the rookieÕs salary overtake MirandaÕs?

 

At the end of 25 years, who received the most money?

 

What is MirandaÕs salary in year n?  What is the rookieÕs?   What is MirandaÕs total at n years?   RookieÕs?

Read and explain their answers.

 

15, 000,000

16,384

 

 

In year 21.

 

 

 

The rookie

 

 

M=1,000,000

R=2^n

m=1,000,000n

r=· i=1n 2n  (they would be able to write this but they should be able to explain it comparing to how they got MirandaÕs total)

                                               

Extend / Elaborate:

Teacher asks other questions not on paper.

 

      

 

So, now whose salary would you pick? What if you only planned to play 10 years?  20 years?  30 years?  Why?   

 

What kind of function does MirandaÕs salary represent?  The rookieÕs?

 

What is a general statement that you can make about exponential and constant functions? 

The RookieÕs.

MirandaÕs.

MirandaÕs.

The RookieÕs?

 

Constant.

Exponential.

 

 

 

   

  Evaluate:

Give other problems using that same kind of scenario.  Have the groups do each of their assigned problems and then present and explain them.

 

 

Students work on the problems and present to the class.

 

Percent effort each team member contributed to this lesson plan:

___%___       ____Name of group member_____________________

 

___%___       ____Name of group member_____________________           

 

Name_________________________

Miranda and the Rookie

Miracle Miranda plays for the California Hoops basketball team. After the Hoops won the WNBA championship, the manager offered her a million dollars a year for the next 25 years, whereas a new rookie for the same team was given $1 the first year, $2 the second year, $4 the third year, and so on, for the next 25 years.

1.                   What is Miranda's salary in year 15? What is the rookie's?

2.                   In which year does the rookie's salary overtake Miranda's?

3.                   At the end of 25 years, who has received the most money?

4.                  What is Miranda's salary in year n? What is the rookie's?