Gotta love those optimistic AP problems

[sniffnoy]

So, doing a practice AP for math homework, I come across the following question:

The spread of a disease in a population is modeled by the differential equation P'(t)=.03P(t)(30-P(t)) where P≤30 is measured in thousands of people. (Presumably there are only 30,000 people in the population.)
Part a asks you to find the general solution, part b to find the specific solution where P(0)=5.

Now part c says "Estimate how many people will eventually have the disease.", that is, find lim[t→∞] P(t). Hm... solve solve solve, crunch crunch crunch, use your common sense and then verify with L'Hopital... (You can do the problem yourself if for whatever perverse reason you actually like this sort of thing...) and we get, lim[t→∞] P(t)=30, that is, "eventually", the entire population will have the disease. Oh goody.

And here they say you can't mention death in school anymore.

-Sniffnoy

--
"I will have a foreign-handed foreign policy."
-George W. Bush

Comments

[fergie142857.livejournal.com]

Umm... all diseases that propagate at a rate proportional to the product of the infected proportion and the healthy proportion eventually infect the whole society. Go logarithmic curves.

[sniffnoy.livejournal.com]

Yeah, I realize that, but it's still funny.