Question

I am really confused as to how I can even approach this differential equation, I really need a step by step solution. Thanks!!

406 Chapter 5 Differential Equations 5 Performance Task Spread of an Influenza Virus Throughout history, influenza viruses have caused pandemics or global epidemics. The influenza pandemic of 1918-1919 occurred in three waves. The first wave occurred in the late spring and summer of 1918, the second wave occurred in the fall of 1918, and the final wave occurred in the spring of 1919. By the time it ended, approximately 21.5 million people across the world had died as a result of the pandemic, with 675,000 deaths in the United States alone. Exercises In Exercises 1-3, use the following information. On a small college campus with 800 students, ten students return from spring break with a contagious flu virus. The rate at which the virus spreads through the campus is given by the differen equation tial A 04 ds dt 800 where S is the number of infected students and t is the number of days. 1. Writing a Logistic Equation Write a logistic equation that models the number of students infected with the virus after t days. Use the equation you wrote in Exercise I 2. Using a Logistic Equation (a) What is lim St)? What does this value represent? How many students are infected with the virus on Day 3? 3. Using a Logistic Differential Equation The slope field for the given differential equation is shown. To print an enlarged copy of the graph, go to MathGraphs.com (b) 600 400 2 00885 48 12 16 20 (a) Sketch the solution that satisfies the initial condition. (b) On what day is the virus spreading most rapidly? How many students are infected with the virus at this point? Justify your answer o) What is the rate of change of the number of students infected with the virus when the virus is spreading most rapidly? Interpret your answer. (d) What are all values of S for which the rate of change of the infected is decreasing? Justify your answer. (e) Repeat Exercise 2(b) using Euler's Method with a step size of1. Compare number of people your results varet!

Answer 1

dS_ニ 0.ysy s ( 800-S) 幺00 S Cs -2o0) L (ds where c ony

800 しttu number