The above chart from Our World in Data (https://ourworldindata.org/coronavirus) shows confirmed cases on the Y-axis and days since 1/21/20 on the X-axis. The reason why we want to graph the Y-axis on a log scale (vs. our normal linear scale) is because we're dealing with something whose growth is exponential in nature (a virus spreading) -- it's not just one person infecting others but all those others infecting others, which are infecting others, and so on.
For the last month in my Algebra 2 classes we've been discussing the inverse relationship between exponential growth and logarithms. Whenever we want to solve for an exponent "x", we convert the equation into a logarithmic equation and solve for "x". Well a virus spreading throughout a population is the perfect time to try to solve for an exponent, since we want to find the growth rate "r" in the exponential growth equation below.
I wondered if I could create a trendline based on the confirmed cases data for Coronavirus. Moreover, if I made this trendline exponential on a log graph, the trendline would be linear (since they're inverses, and an inverse is just a reflection over the line y = x, an exponential graph of a log function will just be a line). Taking the data from Our World in Data and graphing it in Google Sheets, I was able to create the exponential trendline and find the fit (R-squared) and growth rate.
As you can see, the exponential trendlines of a log graph are all lines of different slopes. Looking at their equations (I'll use the United States for example --> y = 0.37*e^(0.145x)) we can see the differences in their slopes as differences in the growth rates in the exponent (since "x" represents time since 1/21/20 in this case). For the United States, this is 0.145, or a 14.5% growth rate, at a R-squared value of 0.823.
The trendline prediction for the United States isn't as accurate as Italy (R-squared of 0.992) or Spain (R-squared of 0.986) since Italy and Spain have seen more community growth and/or have more accurate testing. For the US, I would assume we would have a more accurate trendline (higher R-squared) if we were doing more testing. I would also assume that China and South Korea have a lower R-squared compared to the rest of the top 8 countries since they've worked to reduce the growth rate of the virus through quarantine measures.
Something that I want to bring up: should the world be more worried about Spain right now? They have a growth rate of 31.9% compared to Italy's 22.5% and Iran's 22%. That means Spain's confirmed cases are forecasted to double every 2.17 days compared to Italy's doubling every 3.08 days (or in a week, Spain's cases will be ~9.36x higher than when the week started vs. Italy's ~4.82x growth). I predict we'll hear more about Coronavirus in Spain in the next two weeks.
Semi-related: this great video about exponential growth
