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 is the better deal.
Horizon Cell Phone Company – Base rate=$40 Each additional minute costs $0.05
Vertigo Cell Phone Company – Base rate=$30 Each additional 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 [0,300] or [0,500] 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.
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.
Submit your work as a Word or Rich text format document. Please include all items (graphs, analysis, etc.) all in one document.