Line Graphs and Time Series Screen 7 - Types of Growth

Q&A DQ Courses
#1

Hello,

First, thanks for making great courses I’m enjoying! This is about math and not code - some of the information in Screen 7 isn’t mathematically accurate. It says:

“In the March-July period (thus excluding January and February), Italy had a logarithmic growth in the number of cumulative cases because there were many new cases in the March-April period, but then the number of new cases started to decrease. The line on the graph will become perfectly horizontal when there will be no more new cases.”

This implies that logarithmic growth is asymptotic, but log functions do increase to infinity, just very slowly. There is a similar problem on Screen 8 when what is termed “logarithmic decrease” is shown approaching the x-axis as asymptote. I would argue that this is “exponential decay”.

Also, Brazil’s growth is classed as “exponential”, but it isn’t. It’s increasing faster than linear at the beginning, and then becomes linear from May-July. I worry this reinforces the common misconception that “exponential” means “anything that curves upward at some point”.

I wonder if “faster than linear” and “slower than linear” might be more accurate choices than “exponential” and “logarithmic” to describe growth rates.

Thanks for considering my nitpicking!

#2

I’m another user who had similar concerns on this lesson! (Former math teacher)

I read the first point (Italy’s logarithmic growth becoming horizontal when there are no new cases) as simply a description of how that specific graph will look rather than the general behavior of true logarithmic growth. That specific graph will be horizontal when cases are zero, but it wouldn’t be technically logarithmic anymore. The language is ambiguous enough.

I think calling Brazil’s growth ‘exponential’ is simply because they are focusing on general foundational concepts rather than fully teaching the math, though I understand your concern. As an educator, I can understand the justification for simplifying the math here in order to focus on coding concepts and not overwhelm the learner.

I was concerned about the graph they labelled ‘logarithmic decrease’, though. I actually had to check if using the word ‘decrease’ vs ‘decay’ now connote something different. I agree that it appears to be close to exponential decay. The ‘exponential decrease’ graph is also oddly labelled. I think I see what they are trying to convey, but different wording is needed, at least for that portion, in my opinion.