Real Number and Answer

Zach Snider
Investigative Task:
SPREAD OF DISEASE – The Task

Disease can spread quickly without use of universal precautions. Suppose the spread of a direct contact disease in a stadium is modeled by the exponential equation P(t) = 10,000/(1 + e3-t) where P(t) is the total number of people infected after t hours. (Use the estimate for e (2.718) or the graphing calculator for e in your calculations.)

1. Estimate the initial number of people infected with the disease. Show how you found your answer.

Answer: A total of 474 people would be initially infected.

Equation: p(0)=10,000/(1+3^3) ~ 474.26

2. Assuming the disease does not present symptoms for 24 hours, how many people will have been infected after 3 hours? Show how you found your answer.

Equation: Substitute 3 hours for the time.

Answer: About 5,000 people would be infected in a mere 3 hours.

3. What is the maximum number of people who can become infected? (Note: e(3-t) will approach 0 for very large values of t).
The maximum number of people who could become infected is 10,000.

4. Explain why your answer for Question #3 is the maximum.

Because when you graph the equation you can see it only reaches 10,000.

5. The stadium needs to warn its guests about a rapid disease spread if it affects over 800 people. After how many minutes should the stadium inform its guests of the disease? Show how you found your answer.

After doing the equation you end up with T = 3 - ln(11,5) which gives you the answer T = 0.5575 which is .56 hours. When you divide 60 min/hour you should get the answer 33.46. Meaning the stadium needs 33 minutes to warn its guests.