Project #55888 - Math Project

Part I

Please complete this open ended assessment. Cell phone companies are always claiming to offer a better deal over their competitors. In this exercise, we will compare two cell phone companies’ offers to see which the better deal is.

Horizon Cell Phone Company

Vertigo Cell Phone Company

Base rate=$40

Plus each minute costs $0.05

Base rate=$30

Plus each minute costs $0.07

 

Step 1: Write a linear equation of the form y1=mx+b for the Horizon Cell Phone Company. Graph this equation on the xy-plane and label it as y1. You may use Excel to graph or you can save the graph paper to your desktop and use the 'draw' tools in Word to plot your lines. Be sure to include a large enough set of x-values (something like [0,700] would be suitable. Graphing values only from [0,10] would not yield very much information, since most cell phone users talk for more than 10 minutes each month. Also, be sure to include a title on the graph and labels on the x- and y-axes.

Step 2: Write a linear equation of the form y2=mx+b for the Vertigo Cell Phone Company. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect.

Step 3: Find the point of intersection for y1 and y2 algebraically. Show your work and also plot this point on the graph.

Step 4: Analyze which company offers a cheaper deal on cell phone costs and under what conditions. At what value are they the same?

Step 5: Suppose you talk an average of 200 minutes per month. Which is your best option? What is the difference in price between the two companies' charges for 200 minutes?

As a preview for the final project, your task will be to do steps 6 and 7 below. Part I plays into Part II.

Step 6: Describe another setting in which a systems of equations approach would be useful.

Step 7: Present data and repeat steps 1-5, for an application of your choice. Some ideas may be found by considering examples related to business (supply-demand), nutrition (caloric need vs caloric expenditure), home budget (monthly earnings vs. monthly spending), and/or topics in your professions, other academic courses or those found on the internet. Be sure to cite any sources, if you use outside references for ideas or data.

 

Part II: Final Project

Algebra gives us the means to write an equation or set of equations that model the solution to a problem. Once we have the equations, we have the means of solving all problems of a given type.

Please take a moment to review steps 1 through 5 in part I of the linear systems report. Think about the things you do, the problems you solve. Pick something that involves quantities and write an algebraic model for it.

Ideas to get you started:

  • Sports: For instance, you may track baseball statistics. Can you generalize some of the calculations that are involved? Can you derive a set of calculations on which you might base a prediction of which team will win the World Series?
  • Hobbies: If you make quilts, you use a lot of geometry and algebra. Can you write some equations for what you do? For instance, can you describe the yardage needed in a set of equations? How about the area of each block and the area of the quilt? Is one a function of the other?
  • Business and home finance provide a lot of opportunities to use algebra too. Can you model a business decision algebraically? How about the value of a stock portfolio?
  • Our course may serve a place to look for ideas. Scroll back through our previous modules and view the images for ideas of applications. Reviewing some of our discussions same also provide you with some ideas for projects.
  • Our textbook contains many applications and ideas. You may wish to use one of these to further expand on. (Note: Solving a textbook problem does not meet the requirements for this project. However, exploring a model presented in the book and adding additional analysis, research or data could lead to a wonderful project.)

Assignment:

  • Identify a problem from your own experience that can be modeled algebraically (i.e. with equation(s)). You need to include skills learned from at least two different modules
  • Present the problem (in paragraph form). Describe the important features, variables and assumptions that you are making
  • Create the model for solving the general problem using one or more equation(s). Use your model to solve a specific problem.
  • Present the mathematical calculations that you used. Discuss your model in terms of algebra: are you using functions; is your model linear or non-linear; etc. ? Discuss why and how it all works.
  • Include a graph or graphs
  • Save your file as a Word (.doc or .docx) or Rich Text Format (.rtf) document.

 

For the final project please do all of the following steps:

  1. Describe another setting in which a systems of equations approach would be useful.
  2. Present data for an application of your choice. Some ideas may be found by considering examples related to business (supply-demand), nutrition (caloric need vs caloric expenditure), home budget (monthly earnings vs. monthly spending), and/or topics in your professions, other academic courses or those found on the internet. Be sure to cite any sources, if you use outside references for ideas or data.
  3. Write a linear equation of the form y1=mx+b for your data. Graph these equations on the xy-plane and label it as y1. You may use Excel to graph or you can save the graph paper to your desktop and use the 'draw' tools in Word to plot your lines. Also, be sure to include a title on the graph and labels on the x- and y-axes.
  4. Write a linear equation of the form y2=mx+b for the other equation in your system. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect.
  5. Find the point of intersection for y1 and y2 algebraically. Show your work and also plot this point on the graph.
  6. Analyze the data and explain what the intersection means, in terms of the problem. Is there a 'best' solution to your problem? If so, under what conditions?
  7. Conclude your project with a short summary of what you learned.

Subject Mathematics
Due By (Pacific Time) 02/16/2015 12:00 am
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