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You are watching: Use of polynomials in real life

How many times during your educational career have you thought to yourself, “When on earth am I ever -- and I mean ever -- going to use this?” I would venture to guess we’ve all thought this a time or eight. I know I certainly did. While sometimes this thought held truth (thank you to my college elective, "Poetry of Rap"), other times I realized there were many things I said this about that, in reality, I have found incredibly useful in my career so far. This being my first post as a member of the Finance Council, I find it fitting to salute my education and career, which have brought me to where I am.

There are many items in math and statistics about which I said those exact words throughout the years. The main topics that are top of mind for this are regression, statistical significance, slope, correlation coefficient and the topic of this article: polynomialequations.

Most recently, I have found myself using polynomial equations to both model growth rates and predict monthly revenue. As you can see from that comment, knowing your way around polynomial equations can be useful for anyone who owns a business, anyone interested in owning a business or anyonewhose job revolves around analytics.

For starters, I will define what a polynomial equation is. A polynomial equation is a mathematical expression consisting of variables and coefficients that only involves addition, subtraction, multiplication and non-negative integer exponents of variables. So, a simple example for you would be y=x2+x+1.

I will now walk you through the five steps to modeling growth rate and revenue for your business and how I applied them in my project.

Step 1: Research businesses similar to your own.

This is definitely the place to start. You can do some online digging to find what similar businesses" revenue, or key aspects of revenue, were for particular time periods. This is not only key to understanding how your own business can grow, it also forces your hand to check out possible competitor growth and market information for said competitors. For the project I am working on, I could only find information for year one and years five through seven. Therefore, using a polynomial equation was the obvious choice for modeling what their complete first five years have looked like without that information being public.

Step 2: Quantify how you differ.

The next step is looking at how you differ from the businesses you researched above and how that affects your model. Does your business cover a broader range of products or a narrower range of products? Is geography a factor in what you offer and how you could expand? And, broadly, what can hold you back from growing or catapult your growth in comparison to the businesses similar to you or your competitors? For the project I am working on, the searches and market we would be covering would, in fact, be narrower compared to the similar businesses by products offered.

Step 3: Use a spreadsheet to graph your polynomial.

Now that you have some information about similar businesses and competitors and how you differ, you can use those data points to graph your polynomial in a spreadsheet. With the project I am working on, I had information on only the first year and final three final years, as mentioned above. So, my year one was known, years two through four were unknown and years five through seven were known data points. I used these to graph my polynomial, as well as obtain that polynomial equation to figure out my users for the missing time periods (years two-four). An example is shown below:

By plugging in two, three four for x in your polynomial equation, you are able to figure out your missing user searches.

Step 4: Use "x" as your time period.

In your polynomial equation, x will be your time period. This enables you to figure out what your output is at any given time period. In my project, I had used whole years as my x, as that was all I had. However, I wanted to know what my monthly user searches would be, so I broke that down by one-twelfth to figure out my monthly user searches for the first five years. By doing this, I not only have my expectations of monthly user searches but I also now have a means to see what my month-over-month growth expectations are. In the example we are working with, I will show you year two (months 13-24). This means, for x, you will need to plug in 13/12 for month 13, 14/12 for month 14, etc.

Step 5: Model your revenue.

With many businesses, you not only have your standard modeled growth, but you may have additional sources of revenue that need to be added to figure out your total revenue. For my particular project, that most certainly was the case. Not only did I need to figure out how much revenue would be made per average user search, but I also needed to add revenue from possible partners and affiliates by month. You want to be sure you capture all channels of revenue you expect. Stepping back and thinking on this or talking with a mentor or adviser after your first pass is a great strategy, as you or they may come up with items you had not initially thought of.

With the example we are using, I will calculate the purchase revenue based on the number of users per month we just calculated above, the percent of users that make a purchase, the average purchase price and commission per purchase.

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I certainly hope this has given you an idea of the usefulness and importance of polynomials in business and the real world. And, to all of you students out there, no matter where you are in your education, this post is for you. Because someday, I promise, you will, in fact, use what you have spent all these years learning. Finance Council is an invitation-only organization for executives in successful accounting, financial planning and wealth management firms. Do I qualify?