College Algebra

NAME (Required): _____________________________

Please show all work details with answers, insert the graph, and provide answers to all of the critical thinking questions on this document. Upload this modified Answer Form to the Intellipath Unit 1 Submission lesson. Make sure you submit your work in a modified MS Word document; hand-written work will not be accepted. If you need assistance, please contact your course instructor.

Mathematical Modeling

It is useful to construct a mathematical function that represents observed data. Whether these data are linear, quadratic, rational, radical, exponential, or logarithmic is determined by how they change (i.e., do the observed data change at a constant or variable rate?).

In your corporation’s Information Technology department, a database management system’s hard disk server farm is found to have the expected transaction bit-storage rate characteristics listed below in Table A. Your supervisor has asked you to analyze these data to find the linear equation that best represents these rates. (Any situation in which a variable’s change with respect to a different variable’s unit change ends up always constant can be modeled by a linear function. In either point-slope form, or in slope-intercept form , the constant m is the slope of the line, is the vertical intercept (or y intercept) of the function’s graph, and the ordered pair, , represents some point on the line.)

Given the table below, observations suggest that this hard disk server farm can store megabits of data in microseconds.

For each question, be sure to show all of your work details for full credit. Round all value answers to 3 decimal places.

1. In the table below, based on the first letter of your last name, select 2 pairs of numbers from every one of the ranges in each of the two x and y columns. For example, if your last name starts with M, then you might choose and 20.5). Then, the slope of the line represented by these two points would be: m = (y2 – y1) / (x2 – x1) = (20.5 – 15.6)/(32.5 – 30.2) = 4.9 / 2.3 (rounded to 3 decimal places).

Next, the point-slope equation of that line is y – 15.6 = 2.13(x – 30.2), while the slope-intercept form is y = 2.13x – 48.726.

Here, x is the independent or horizontal variable, and y is the dependent or vertical variable. A negative amount of time indicates latency in the system.

Use your 2 chosen values (other than the ones chosen above) to answer this and the following questions below.

Table A – Observations of bit-storage amounts and times.

In the table below, type your 2 selected pairs of points based on your last name. (10 points)

2. Use the 2 selected ordered pairs from Part 1 to construct a linear function model in first the point-slope form, and then convert that equation to slope-intercept form for this hard disk server farm’s bit-storage equation. Show all of the work details for constructing both linear function forms. (20 points)

Explain your answer here:

3. Graph your bit-storage function using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Microsoft’s Mathematics 4.0, online utilities like desmos.com, and many others.)

Insert both the function and the graph into the Word document containing your answers and work details. Be sure to label and number the axes appropriately so that the graph matches the chosen and calculated values from above. Also, make sure the graph contains the vertical and horizontal intercepts for your linear function.

Bar charts, pie graphs, and similar data displays are NOT appropriate as graphs of functions in this course. Correctly constructed, your graph will be a straight line, hence the name linear function. If you are using Excel, then make sure that you use the Scatter with Smooth Lines and Markers feature in the Insert tab under the Charts menu on the Word ribbon. (20 points)

Insert both your graph and function here:

4. Based on your model bit-storage function, how many microseconds will it take for your model to store 200 megabits? Show all of the work details. (20 points)

Explain your answer here:

5. How many megabits can your model’s linear bit-storage function store in 400 microseconds?

Linear forecasting is the process of extrapolating the given function values to an independent variable value that is not observed in the data. In this question, assuming the hard disk server farm performs at the same rate at longer times, you are predicting or forecasting the number of megabits that can be stored in 400 microseconds without actually collecting any data at that range.

Show all of the work details. (20 points)

Explain your answer here:

6. As the company grows and needs faster bit-storage rates, it will expand its operations. How can this linear function model and the information it predicts with linear forecasting help to plan for optimization or scaling of the future requirements for the hard disk server farm? (10 points)

Explain your answer here:

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