Your students' example has no real or mathematical basis, so it's obvious that "artificially forcing this value to be an integer makes it impossible to express the results - day-0 (1 student), day-1 (2 students), day-2 (4 students)—in a mathematical function".

"It's growing at the rate of 1.5 students/day" seems like nonsense; in your example this growth rate must necessarily be an integer, not a decimal. If it made sense, you should be able to give teachers a list of their students on day one or day three, etc. Are you able to do that? IMHO your example is mathematically ill-posed.

"...the author means 'selectively ignore the principles of mathematics.'" Never. The author simply recalls that some quantities can't be measured by decimal numbers.

"...but because it misunderstands math and it uses that misunderstanding to mislead people trying to code into thinking their code is wrong..."
It's a trial of intent and I assert to be a good mathematician (even if I am getting old....).

@adamgosnell : you are free to consider that there is an issue but I don't.
The calculation is conform to the different results given by tables about population statistics. See for example:
"Global annual population growth" at https://en.wikipedia.org/wiki/World_population#Annual_population_growth.
Besides that a clear hint is given in the description.
@zac4code : thanks for your explanation and thanks for your thanks.