# LASA 2: Exponential Growth

**PLEASE READ EACH STEP COMPLETELY BEFORE STARTING THAT STEP!!!!!**

Step 1: Identify the population. (Where, what, how much) An example would be that you are looking at the population of telephones in the world. As of 1900, there were 40,000 telephones in the wild. I believe that the tiger population is growing by 28% each year. You must have a reference for the information. You can make up the statistics, but then you will have to make up a reference as well. You may look up a reference online if you wish and cite that. AGAIN â€“ YOU CAN MAKE IT UP, BUT MAKE UP A REFERENCE THAT SOUNDS GOOD!

Step 2: Identify the starting year and the population at that time. (your beginning year will be â€œ0â€ in your excel chart) For my example, the starting year would be 1900; this would represent 0. THE ACTUAL YEAR DOES NOT GO IN THE EXCEL CHART.

Step 3: Open an excel chart and a word document. You will use the excel chart to create a graph and the word document to write the paper. You will be copying the excel chart into your final paper.

Step 4: In the excel chart, put the year increments in column A. The first entry will be 0 (your beginning year). You decide if you want to go in 2, 3, or 5 (etc.) year increments. If 2, then your next 4 numbers in the A column would be 0, 2, 4, 6, 8â€¦.if 3 then 0, 3, 6, 9, 12â€¦.if 5 then 0, 5, 10, 15, 20. My paper only uses 3 year differences â€“ you must use 4!!! There will be a total of 5 numbers (starting with 0) in your â€œAâ€ column.

Step 5: To get the â€œBâ€ column, you will go to the calculator on the computer. You will need to click on view and set the calculator to scientific view.

Next, on the calculator you will:

Year (from column A) times percent you have (as a decimal) then hit equal. Then hit the INV button (top left of calculator) and the e^{x} button (next to INV). Now hit times and then your starting value. This number goes in column â€œBâ€ next to the year you used.

Note â€“ the only thing that changes each time is the year (from column A). DO NOT CHANGE THE VALUE AT THE END. IT IS ALWAYS YOUR STARTING NUMBER.

If THE CALCULATIONS CONFUSE YOU, GO TO http://www.investopedia.com/calculator/fvcal.aspx AND USE THAT WEBSITE TO FIND THE NUMBER IN COLUMN B FOR EACH YEAR INCREMENT YOU HAVE. THE PERCENT WILL STAY THE SAME, THE PRESENT VALUE WILL STAY THE SAME, BUT YOU JUST CHANGE THE YEARS!!!!!

Step 7: Have Excel make a scatter plot (like you did in the first LASA â€“ see the â€œDoc Sharing notes if needed)of the two columns. Nowâ€¦go to Layout and click â€œLegendâ€ and select none.

Step 8: In the Layout tab, click â€œAxis Titleâ€ the Horizontal and â€œTitle Below Axisâ€ and vertical and select â€œVertical Titleâ€.

Step 9: Now, in each axis title, you can highlight â€œAxis Titleâ€ and replace the horizontal with â€œYearsâ€ and the vertical with â€œPopulationâ€.

Step 8: By right clicking on one of the points on the scatterplot, add a â€œTrendlineâ€. While On the â€œAdd Trendlineâ€ option, have Excel display the equation for the line onto the chart and have it display R^{2} on the chart. Also, while formatting the trendline, up at the top â€“ click on exponential. This will make your line a curve. Excel, have it graph the line on the chart (like you did last class).

Step 9: Remember that R^{2} * 100 gives us the percentage of growth implications due to time. With this in mind, make an interpretation based on your graph. Your interpretation should be more than a mere 1 sentence statement.

Step 10: What are the likelihood of your results? Would it be expected that the percent growth rate would stay constant over such long periods? Would the growth rate change exponentially (like doubling each year) more than it would be just a constant growth? What other changes could affect the growth?

Step 12: Write it up in a neat paper with the graph copied and pasted into the paper. If you got the population from a web-source, be sure to sight that source.

PLEASE READ MY PAPER EXAMPLE BEFORE YOU START WRITING YOURS. IT WILL GIVE YOU AN IDEA OF HOW TO GO ABOUT YOUR PAPER. ALSOâ€¦.MAKE SURE TO PASTE YOUR EXCEL CHART INTO THE PAPER. ONLY PASTE THE SCATTERPLOT â€“ **NOT** THE COLUMNS!!!!

Your paper should follow the format of my paper. You will not be required to submit a separate title page or reference page. Simply use the same format and set up that I did.

Trends in Online Education Growth

According to James Marshall Crottyâ€™s Forbes Magazine article, â€œOver 5.6 million people enrolled in at least one online course in 2009â€ (Crotty, 2012, p. 1). Crotty goes on to state the growth in online enrollment is 21% (Crotty, 2012). This article lends the population of online learners with a growth of 21%. I decided to look at this trend for a five, ten, and fifteen year span of time.

Using Crottyâ€™s growth percentage, we can see that online enrollment is expected to explode in the next fifteen years. Exponentially, the population in five years would reach approximately 16 million. The population would continue to climb to approximately 45.7 million in ten years and approximately 130.7 million in fifteen years. From a graphical standpoint, the growth is more obvious.

If trends in education continue to follow this growth pattern, it seems that there is an exponential surge occurring in the online arena. This growth does seem to be in line with the ideals that many Americans are trying to balance more time demands with career and family obligations while attending college. While I believe that online education does have a growth pattern that is exponential, I feel that there will be a time when the growth slows. There will be adjustments for availability of online opportunities, costs of higher education, and simply that there are fewer people who will be attending college. Also, there will be surges in the pattern as resources become more plentiful, economic hardships become less burdensome, and individuals seek alternative income methods. More than just the availability will impact the growth of the online environment. It is affected by the student population, the economy, and the progress of programs that are offered in online arenas. For this reason, the growth may not remain at a constant 21% throughout the next fifteen years.

References

Crotty, J. M. (2012). *Future Of Education Is Mobile, Social, and in the Cloud: Lessons from EduCause.* Retrieved from Forbes.com : http://www.forbes.com/sites/jamesmarshallcrotty/2011/10/25/future-of-education-is-mobile-social-and-in-the-cloud-lessons-from-educause-part-one/

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