My AP Calculus Extra Credit Problem
Once upon a time, there was a buffalo soldier with saliently long dreadlocks. He was driven from Africa to the heart of America, but little did he know that his dreadlocks carried the parainfluenza virus, a virus that serves to cause the common cold.
One day, while he was standing in line at his local coffee shop awaiting the preparation of the cafe mocha he'd long sought to buy and sip, one of his dreadlocks came in contact with a cup of coffee near him which was destined to belong to Joel, a successful businessman. Joel squealed at the sight, alarmed. The buffalo soldier apologetically said, "Don't worry, be happy, man!"
Joel growled skeptically, "Oh, well, I'll be late for work if I don't hurry, " and quickly gulped the cup of coffee.
Two days later, at the office, Joel started experiencing the symptoms of the cold. He sneezed vigorously and continuously, and when Matt, the fellow who worked in the office nextdoor, approached him with a pot of coffee, Joel was glad to receive him. The two commenced engaging in profound conversation when Matt exclaimed, "Oh! I forgot the sugar! I'll go get it. I shall return." Joel sneezed again, this time in the pot of coffee. He thought, "Don't worry, be happy, man!" and failed to mention the incident to Matt upon his return.
Matt poured himself a cupfull of the coffee, drank it, and marveled, "Boy, is this coffee great or what?!" His secretary Kimberly asked to try some, and Matt happily poured her a cup.
Soon enough, the vast majority of the 21st floor of the building had had coffee from the pot. There was a mutual appreciation for the coffee, and when Jay the psychic biochemist was told to have a mugfull, he felt an evil aura about the coffee. He obtained a sample of the coffee and analyzed it under a powerful microscope. After a few minutes, he remarked, "This coffee is loaded with dead white blood cells-- with snot carrying the common cold virus!!"
Panick-stricken, all who had drunk the coffee turned to Joel and, with clenched fists, gnarled, "Thou shall suffer!!!"
Joel initially had 6000 viral bacteria in him. Assume that 90% of the bacteria wound up in the coffee pot. Given that the bacteria grows exponentially from 2000 to 4000 units in 20 minutes, that the coffee party lasted 2 hours, that the individuals' immune systems were fairly weak, and that each person could only withstand an infection of 6000 bacteria before dying, how many people did Joel need to escape from in order to avoid being lynched and surviving?
Credits: Bob Marley and the common cold
And yes, I do claim a copyright on this. Don't steal my problem!! I have a mean cat to hurt you if you do!!!
One day, while he was standing in line at his local coffee shop awaiting the preparation of the cafe mocha he'd long sought to buy and sip, one of his dreadlocks came in contact with a cup of coffee near him which was destined to belong to Joel, a successful businessman. Joel squealed at the sight, alarmed. The buffalo soldier apologetically said, "Don't worry, be happy, man!"
Joel growled skeptically, "Oh, well, I'll be late for work if I don't hurry, " and quickly gulped the cup of coffee.
Two days later, at the office, Joel started experiencing the symptoms of the cold. He sneezed vigorously and continuously, and when Matt, the fellow who worked in the office nextdoor, approached him with a pot of coffee, Joel was glad to receive him. The two commenced engaging in profound conversation when Matt exclaimed, "Oh! I forgot the sugar! I'll go get it. I shall return." Joel sneezed again, this time in the pot of coffee. He thought, "Don't worry, be happy, man!" and failed to mention the incident to Matt upon his return.
Matt poured himself a cupfull of the coffee, drank it, and marveled, "Boy, is this coffee great or what?!" His secretary Kimberly asked to try some, and Matt happily poured her a cup.
Soon enough, the vast majority of the 21st floor of the building had had coffee from the pot. There was a mutual appreciation for the coffee, and when Jay the psychic biochemist was told to have a mugfull, he felt an evil aura about the coffee. He obtained a sample of the coffee and analyzed it under a powerful microscope. After a few minutes, he remarked, "This coffee is loaded with dead white blood cells-- with snot carrying the common cold virus!!"
Panick-stricken, all who had drunk the coffee turned to Joel and, with clenched fists, gnarled, "Thou shall suffer!!!"
Joel initially had 6000 viral bacteria in him. Assume that 90% of the bacteria wound up in the coffee pot. Given that the bacteria grows exponentially from 2000 to 4000 units in 20 minutes, that the coffee party lasted 2 hours, that the individuals' immune systems were fairly weak, and that each person could only withstand an infection of 6000 bacteria before dying, how many people did Joel need to escape from in order to avoid being lynched and surviving?
Credits: Bob Marley and the common cold
And yes, I do claim a copyright on this. Don't steal my problem!! I have a mean cat to hurt you if you do!!!
Francesca contentedly consumes her coffee at 8:42:00 PM
