Continuous Everywhere but Differentiable Nowhere



Name:_______________________ Date assigned:______________ Band:________Calculus | Packer Collegiate Institute Vomitorium: Shaping Up or Shipping OutINFECTION!Oh dear! A horrible stomach bug has been going around the senior class at Packer. It started at the Senior Lock In, when Ms. Connell came to school feeling sick. And others got sick, slowly but surely. And by the end of the awful infection, the entire senior class was vomiting. Gross.We’re going to model this… with some assumptions.Once you’re infected, you never get cured. You will throw up forever.Once you’re infected, you have the potential to infect at most one other person each 15 minutes.Instead of saying there are 71 students (+ Ms. Connell) in the senior class, let’s say there are only 29 students in the senior class (+ Ms. Connell).We could do this model with all the students in the senior class, but it would take too long! So let’s get a general idea of what’s going on with just 30 people.Now, you are hopefully thinking, these assumptions are simplistic. I mean, you won’t vomit forever from a stomach bug – you recover. And some people are more immune from diseases than others. Those who model infectious diseases have more complicated assumptions, and then create a model from these assumptions. But honestly, the math doesn’t get to different than what we’re doing… just more considerations are put into the model.We’ll assign each student, and Ms. Connell a number. Ms. Connell will be #1 and the students will be #2 to #30.123456789101112131415161718192021222324252627282930When it is 6pm (when senior lock in begins), Ms. Connell is the only one sick. So cross out #1. And fill in the first line of the table on the next page.Now take out your graphing calculator. We’re going to get some kids vomiting! Let’s find out who gets infected at 6:15…TimeNumber of People Infected6:00pm16:15pm6:30pm6:45pm7:00pm7:15pm7:30pm7:45pm8:00pm8:15pm8:30pm8:45pm9:00pm9:15pm9:30pm9:45pm10:00pmMATH > PRB > 5:randInt… and then type … What that command does is pick a single random integer between 1 and 30. So you found who was infected at 6:15pm! Cross that person out (they are now sick!) on the chart on the first page. Now two people are infected… so each has a chance of infecting someone else… So to find out who is infected at 6:30pm, you will type. This will give you two random numbers between 1 and 30. You continue this process, until all the people in the class are infected. Fill in the chart with the number of people infected – but be careful! Read Warning! Sometimes you will get a number using the random number generator that is already crossed out. For example, you might get #1 (Ms. Connell) show up. Since she’s already infected, you don’t do anything. The number of infected won’t always double… because sometimes an infected person infects another infected person…Now graph the data! Label the x-axis with the time – and gently draw the curve…Some questions to get you thinking! What happens at the beginning of the spread of the disease? Can you see a general (but maybe not perfect) pattern to the numbers at the beginning? When did the pattern break? When were about half the people infected? Was that about half the time it took for all the people to be infected?You are a person sent from the CDC to analyze this data and explain what happened. Write a report (it doesn’t have to be in paragraph form! you can use bullet points) explaining the evolution of the infection (from start to disgusting finish) for Dr. Dennis. Remember, you want to explain it in layman’s terms, because Dr. Dennis isn’t a calculete! Now explain your findings using mathematical / calculus terms, for Mr. Shah and your boss at the CDC. Logistic Function: Read the Wikipedia page on the logistic function []. ................
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