Week 5 Assignment

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 5 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.

In this assignment, you will study an exponential function that is similar to Moore’s law that was formulated by Dr. Gordon Moore.

The following is a table that represents the actual number of transistors for Premium CPU chips between the years 1971 and 2017:

If you let equal the number of years after 1971 (the year 1971 means ), then these data can be mathematically modeled by the exponential function

For each question, be sure to show all of your work details for full credit. Round final answers to the nearest whole value.

1. Graph your function using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Microsoft’s Mathematics 4.0; or online utilities like desmos.com; and there are many others.) Use axes scales of -10 < x < 20 and -10,000 < y < 200,000 in order for the graph to show up properly in the viewing window.

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. (20 points)

Insert both your graph and function here:

2. Based on this function, what would be the predicted transistor count for the years 2006 and 2017? Show all of the calculation details. (20 points)

Explain your answer here:

3. Using the table above, find the actual transistor count in the years 2006 and 2017 for Premium CPU chips. Compare these values to the values predicted by the function in part 2. Are the actual values over or under the predicted values? By how much? Explain what this information means in terms of the following mathematical model function:

Show the graphed table points along with the graphed function. Do the points fall on the predicted curve? Does it appear that the functions that were created to be best-fit functions for empirical chronological data are good at predicting future values? (20 points)

Insert both your explanation and graph here:

4. For what value of will the function predict the value ? Show all of the calculation details. (20 points)

Explain your answer here:

5. Examine the connection between the exponential and logarithmic forms to your problem.

First, for if and only if both equations give the exact same relationship among x, y, and b.

Next, use the rule of logarithms, .

Applying the given relations, convert the function, , into logarithmic form.

Then, examine the function, . Discuss this conversion, and demonstrate the inverse function relationship between the functions and with graphs. (20 points)

Insert both your explanation and graphs here:

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