The Math Behind “Going Viral”
As we continue to explore everyday items and concepts that are made with math, this week we are exploring the concept of going viral. I’m sure you remember the star-studded selfie from the 2014 Academy Awards in which an Ellen Degeneres tweet nearly broke the Internet. Within hours it became one of the most-retweeted posts in Twitter’s history, garnering more than 3.3 million retweets.
Which brings me to the question, what exactly does it mean to “go viral? By definition, it means that, on average, every time one person engages with your tweet, they share it and compel at least one other person to share it to their followers as well. This is exponential growth at its finest. We have a quick video that helps explain the concept to your students:
Now, let’s imagine for a moment that you find this blog post and video so compelling (we’re pretending here) that you tweet the link to your followers. You are known as the first generation to check out this blog post on our website. Later in the day, three teachers who were looking for lessons on exponential growth on Twitter see your post, like it and share the link with their followers. Those three teachers are the second generation. From their shares, 50 other people visit our website (third generation). By Wednesday, we’re on our 27th generation, and 10,000 people have visited our website, and my boss is begging me to write more stories on exponential growth!
In all seriousness, what’s important about this example? Each generation contained more people than the generation before. That means that instead of reaching fewer and fewer people as time passed, our video reaches more and more students as time goes on. Below are a few additional examples of exponential growth activities you can try with your students as we continue to connect math to every day concepts.
Exponential Growth: In this algebra II activity, students explore the exponential function y=b^x for different values of b. Students then use a line tangent to the curve at a point to explore the relationship between the slope of the tangent line at that point and the value of the function at the same point. At the end of this activity, students will discover that there is exactly one value of b, Euler’s number, for which the slope of the tangent and value of the function are equal.
Spreading Doom: In this activity, students are introduced to the geometric sequence that models the spread of a virus. Students will relate the growth model to an exponential curve.
Coin Toss: Students will run two experiments that simulate pouring out coins from a bag. Students will collect data and model the data with different methods for determining the exponential equations.
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