Sociologists have found that a rumor tends to spread at a rate in direct proportion to the number x who have heard it and to the number P - x who have not, where P is the total population (logistic growth). If a resident of a 400-student dormitory hears a rumor that there is a case of TB on campus, then P = 400 and

where t is time (in minutes). Use the slope field to answer the following questions.

(A) How many people have heard the rumor after 15 minutes?

(B) To the nearest minute, when will 100 people have heard the rumor?

(C) When is the rumor spreading the fastest?

Transcribed Image Text:

dx 0.001x(400 – x) x(0) = 1 dt