Spreading the News Problem: You arrive at school and meet your mathematics teacher, who

Chapter 7, Problem 3

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Spreading the News Problem: You arrive at school and meet your mathematics teacher, who tells you todays test has been cancelled! You and your friend spread the good news. The table shows the number of students, y, who have heard the news after x minutes have passed since you and your friend heard the news. x (min) y (students) 0 2 10 5 20 13 30 35 40 a. Plot the points. Imagine a function fit to the points. Is the graph of this function concave up or concave down or both? b. There are 1220 students in the school. Use the numbers of students at 0 minutes and at 40 minutes to find the equation of the logistic function that meets these constraints. c. Plot the graph of the logistic function for the first three hours. d. Based on the logistic model, how many students have heard the news at 9:00 a.m. if you heard it at 8:00 a.m.? How long will it be until all but 10 students have heard the news?